{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Eigenvectors and Eigenvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "internals": {},
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format='retina'\n",
    "# import libraries\n",
    "import numpy as np\n",
    "import matplotlib as mp\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import laUtilities as ut\n",
    "import slideUtilities as sl\n",
    "import demoUtilities as dm\n",
    "import pandas as pd\n",
    "from importlib import reload\n",
    "from datetime import datetime\n",
    "from IPython.display import Image\n",
    "from IPython.display import display_html\n",
    "from IPython.display import display\n",
    "from IPython.display import Math\n",
    "from IPython.display import Latex\n",
    "from IPython.display import HTML\n",
    "print('')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "internals": {},
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       " .container.slides .celltoolbar, .container.slides .hide-in-slideshow {\n",
       "    display: None ! important;\n",
       "}\n",
       "</style>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%html\n",
    "<style>\n",
    " .container.slides .celltoolbar, .container.slides .hide-in-slideshow {\n",
    "    display: None ! important;\n",
    "}\n",
    "</style>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {},
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "%Set up useful MathJax (Latex) macros.\n",
    "%See http://docs.mathjax.org/en/latest/tex.html#defining-tex-macros\n",
    "%These are for use in the slideshow\n",
    "$\\newcommand{\\mat}[1]{\\left[\\begin{array}#1\\end{array}\\right]}$\n",
    "$\\newcommand{\\vx}{{\\mathbf x}}$\n",
    "$\\newcommand{\\hx}{\\hat{\\mathbf x}}$\n",
    "$\\newcommand{\\vbt}{{\\mathbf\\beta}}$\n",
    "$\\newcommand{\\vy}{{\\mathbf y}}$\n",
    "$\\newcommand{\\vz}{{\\mathbf z}}$\n",
    "$\\newcommand{\\R}{{\\mathbb{R}}}$\n",
    "$\\newcommand{\\vu}{{\\mathbf u}}$\n",
    "$\\newcommand{\\vv}{{\\mathbf v}}$\n",
    "$\\newcommand{\\vw}{{\\mathbf w}}$\n",
    "$\\newcommand{\\col}{{\\operatorname{Col}}}$\n",
    "$\\newcommand{\\nul}{{\\operatorname{Nul}}}$\n",
    "$\\newcommand{\\vb}{{\\mathbf b}}$\n",
    "$\\newcommand{\\va}{{\\mathbf a}}$\n",
    "$\\newcommand{\\ve}{{\\mathbf e}}$\n",
    "$\\newcommand{\\setb}{{\\mathcal{B}}}$\n",
    "$\\newcommand{\\rank}{{\\operatorname{rank}}}$\n",
    "$\\newcommand{\\vp}{{\\mathbf p}}$"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "internals": {
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "\\newcommand{\\mat}[1]{\\left[\\begin{array}#1\\end{array}\\right]}\n",
    "\\newcommand{\\vx}{{\\mathbf x}}\n",
    "\\newcommand{\\hx}{\\hat{\\mathbf x}}\n",
    "\\newcommand{\\vbt}{{\\mathbf\\beta}}\n",
    "\\newcommand{\\vy}{{\\mathbf y}}\n",
    "\\newcommand{\\vz}{{\\mathbf z}}\n",
    "\\newcommand{\\vb}{{\\mathbf b}}\n",
    "\\newcommand{\\vu}{{\\mathbf u}}\n",
    "\\newcommand{\\vv}{{\\mathbf v}}\n",
    "\\newcommand{\\vw}{{\\mathbf w}}\n",
    "\\newcommand{\\va}{{\\mathbf a}}\n",
    "\\newcommand{\\ve}{{\\mathbf e}}\n",
    "\\newcommand{\\vp}{{\\mathbf p}}\n",
    "\\newcommand{\\R}{{\\mathbb{R}}}\n",
    "\\newcommand{\\col}{{\\operatorname{Col}}}\n",
    "\\newcommand{\\nul}{{\\operatorname{Nul}}}\n",
    "\\newcommand{\\rank}{{\\operatorname{rank}}}\n",
    "\\newcommand{\\setb}{{\\mathcal{B}}}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"28d5ce621994b7e6\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#28d5ce621994b7e6\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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zv5ej610rbriIiIi0Fw7cBJyfdkNE0lSLmXv/k5Cjv3cZtbl7EP75Ck3QsYIw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\n/wcvFt0jfOhxIwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1123abdd8>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 271,
       "width": 383
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "cohortMatrix = np.array([\n",
    "[56, 42, 49, 39, 40, 31, 33, 46, 55, 91, 83],\n",
    "[43, 36, 27, 34, 24, 29, 39, 56, 74, 69, 111],\n",
    "[32, 24, 22, 21, 26, 25, 44, 64, 52, 77, 105],\n",
    "[25, 16, 19, 28, 24, 30, 37, 40, 49, 56, 79]])\n",
    "nyears = np.shape(cohortMatrix)[1]\n",
    "# index rows by time, and columns by cohort    \n",
    "Year = pd.DateOffset(years=1)\n",
    "# need to fliplr because spreadsheet rows are in decreasing cohort order\n",
    "datestrs=['09-2004','09-2005','09-2006','09-2007','09-2008','09-2009','09-2010','09-2011','09-2012','09-2013','09-2014','09-2015']\n",
    "dates = [datetime.strptime(x, '%m-%Y') for x in datestrs[:nyears]]\n",
    "cohorts = pd.DataFrame(np.fliplr(cohortMatrix.T),index=dates,columns=pd.Index(['U1','U2','U3','U4']))\n",
    "# learning the model\n",
    "b = np.array(cohorts[1:])\n",
    "a = np.array(cohorts[:-1])\n",
    "x, resid, rank, s = np.linalg.lstsq(a,b)\n",
    "A = x.T\n",
    "#\n",
    "cohorts.sum(axis=1).plot()\n",
    "plt.ylim(ymin=0)\n",
    "# plt.legend(['Model','Actual'],loc='best')\n",
    "plt.title('Number of BU CS Majors',size=20)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Currently the number of CS majors is growing very rapidly.  We'd like to have some estimate of where the numbers might be going.\n",
    "\n",
    "Modeling the number of students in the CS major is challenging because students enter and leave the major at various points during their undergraduate degree."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We will use a simple linear model that we will train on historical data. \n",
    "\n",
    "Our state variable is \n",
    "\n",
    "$$\\vx_t = \\mat{{r}x_{1,t}\\\\ x_{2,t}\\\\ x_{3,t}\\\\ x_{4,t}}$$\n",
    "\n",
    "where $x_{i,t}$ is the number of students who are declared CS majors and in their $i$th year at BU, in the fall of year $t$.   Our model is a linear dynamical system (or linear recurrence):\n",
    "\n",
    "$$ \\vx_{t+1} = A \\vx_t.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Given historical data which are measurements of our state variable from past years, we can estimate $A$ by a method called _least squares_ (which we will cover later in the semester.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "To give you a sense of how the number of students of different classes varies depending on the situation, here are three examples, corresponding to shrinking, early growth, and steady growth:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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9K/AL4MQuP7Nflplfbj3JzP+KiFMot1X/74j4FGUkkhdTRhV57XwFtjTJBi6yM/PnEbEH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\nSZIkNcwhW5IkSWqYQ7YkSZLUsP8DwJE117yWf6cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1123b6b38>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 268,
       "width": 364
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "plt.subplot(1,3,1)\n",
    "cohorts.iloc[0].plot(kind='bar')\n",
    "plt.title(cohorts.index[0].strftime('%Y'))\n",
    "plt.subplot(1,3,2)\n",
    "cohorts.iloc[6].plot(kind='bar')\n",
    "plt.title(cohorts.index[6].strftime('%Y'))\n",
    "plt.subplot(1,3,3)\n",
    "cohorts.iloc[10].plot(kind='bar')\n",
    "plt.title(cohorts.index[10].strftime('%Y'))\n",
    "plt.subplots_adjust(wspace=0.7)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "So, given enough historical information in the form of this state vector over previous years, we can in fact make accurate predictions of number of CS majors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"75f3d45250b76108\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#75f3d45250b76108\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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gQc7rZ5/1/VDuKY2Yi4iIiEiWOJtwlpiEGIoFF8tU+2+/hQcfhJIlndHyIkVc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\noGAuIiIiIuID/w9IREKCfd7aFwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1130c83c8>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 255,
       "width": 371
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "OneYearAhead = cohorts.dot(A.T).shift(1,freq=Year)\n",
    "OneYearAhead.columns=pd.Index(['U1','U2','U3','U4'])\n",
    "OneYearAhead.sum(axis=1).plot()\n",
    "cohorts.sum(axis=1).plot()\n",
    "plt.ylim(ymin=0)\n",
    "plt.legend(['Model','Actual'],loc='best')\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Besides predicting next year's class sizes, analyzing this model can help us answer other important questions: \n",
    "\n",
    "1. If CS major enrollments were at steady-state, how many students will be Freshmen, Sophomores, etc?  (This impacts course offerings).\n",
    "2. If the CS major were at steady-state, how many students would be graduating each year?\n",
    "3. What is the intrinsic growth rate predicted by this model?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Today's lecture will start to develop the tools to answer such questions (and more)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Eigenvectors and Eigenvalues"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The system above is an example of a linear transformation $\\vx\\mapsto A\\vx.$  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "As we've seen, such transformations, thinking geometrically, can move a vector to a new location."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Let's start with a simple example: a __shear__ matrix:\n",
    "\n",
    "$$ A = \\mat{{rr}1&0.1\\\\0&1} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Let's look at what this matrix does to each point in the plane."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x113169e48>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 460,
       "width": 683
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = np.array([[1, 0.1],\n",
    "              [0,   1]])\n",
    "ax = ut.plotSetup(-7,7,-7, 7, size=(12,8))\n",
    "ut.centerAxes(ax)\n",
    "for x in range(-6,7):\n",
    "    for y in range(-6,7):\n",
    "        v = np.array([x,y])\n",
    "        ut.plotVec(ax, v)\n",
    "        ut.plotVec(ax, A.dot(v),'b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We can use arrows to show how each red point is moved to the corresponding blue point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"5e7d6a85c2cbfa9b\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#5e7d6a85c2cbfa9b\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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cM3/9618X+fv3WWaZ/Lif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1+9/mVwOp3kuuuSk09OPvax0tMwS8wrPcDQ6HSSf//3ZHQ0WbYs+clPqo8fcEDZudriySeTyy+v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\nf3M6XSc4/txyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1131ab630>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 460,
       "width": 683
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "ax = ut.plotSetup(-7,7,-7, 7, size=(12,8))\n",
    "ut.centerAxes(ax)\n",
    "A = np.array([[1,0.1],[0,1]])\n",
    "for x in range(-6,7):\n",
    "    for y in range(-6,7):\n",
    "        ut.plotArrowVec(ax, A.dot(np.array([x,y])), [x,y])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Now let's look at a more complicated situation.\n",
    "\n",
    "Consider the matrix $A = \\mat{{rr}1.0&0.2\\\\0.1&0.9}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"c4171153ae8c76cd\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#c4171153ae8c76cd\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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NHRs+/sortpIz3EPI6n2p7su6ebOdgCpXLrntQJoxw0667tghKSRclezvm59f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\nhZhBcjWaNGggTZli3fFGjJDat7fueE7j6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XJl81q2aZPpP4nIcLm877U1a0pff21vPE6T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\ngsij/2qsIbkKAACA2EFyFWHnq3o1O1S3Wm/wYGn69MBvd/HF0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yJXx48DL7wATJ3q+ua/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7bdPTJbT76CMeiq6XBg2AyZOB6tWlWsifYBUArr2W7QLMKiZGvvQ5edJ1e+vWMtDszBlj1mV1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\nAAByR14oFHL6WMcPBAAAAJKR9+O09DSOWQEAAIBk5aX6AHquAgA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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11304eba8>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 460,
       "width": 683
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "V = np.array([[2,-1],[1,1]])\n",
    "L = np.array([[1.1,0],\n",
    "              [0,0.8]])\n",
    "A = V.dot(L).dot(np.linalg.inv(V))\n",
    "ax = ut.plotSetup(-7,7,-7, 7, size=(12,8))\n",
    "ut.centerAxes(ax)\n",
    "for x in range(-6,7):\n",
    "    for y in range(-6,7):\n",
    "        v = np.array([x,y])\n",
    "        ut.plotArrowVec(ax, A.dot(v), v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The starting point for understanding such systems is to look for special vectors which __do not change their direction__ when multiplied by $A$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Example.__\n",
    "\n",
    "Let $A = \\mat{{rr}3&-2\\\\1&0}, \\vu = \\mat{{r}-1\\\\1}, \\vv=\\mat{{r}2\\\\1}.$  The images of $\\vu$ and $\\vv$ under multiplication by $A$ are shown here:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div id=\"9e2897df81507043\"></div>\n",
       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
       "            var p = $(\"#9e2897df81507043\");\n",
       "            if (p.length==0) return;\n",
       "\n",
       "            while (!p.hasClass(\"cell\")) {\n",
       "                p=p.parent();\n",
       "\n",
       "                if (p.prop(\"tagName\") ==\"body\") return;\n",
       "            }\n",
       "            var cell = p;\n",
       "            cell.find(\".input\").addClass(\"hide-in-slideshow\")\n",
       "        });\n",
       "    </script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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emTdvXg444IBMmzat0d/CuGjRAjBWlWq12sj7NfRmAAB0nkqlkiRp8PtcYAg/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\nsv8fU+Mf8oGILswAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113543d30>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 470,
       "width": 693
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "reload(ut)\n",
    "ax = ut.plotSetup(size=(12,8))\n",
    "ut.centerAxes(ax)\n",
    "A = np.array([[3,-2],[1,0]])\n",
    "u = np.array([-1,1])\n",
    "v = np.array([2,1])\n",
    "#\n",
    "ut.plotArrowVec(ax, v, [0,0], color='Blue')\n",
    "ut.plotArrowVec(ax, A.dot(v), [0,0], color='Blue')\n",
    "ax.text(v[0],v[1]+0.2,r'${\\bf v}$',size=20)\n",
    "ax.text(A.dot(v)[0],A.dot(v)[1]+0.2,r'$A{\\bf v}$',size=20)\n",
    "#\n",
    "ut.plotArrowVec(ax, u, [0,0], color='Red')\n",
    "ut.plotArrowVec(ax, A.dot(u), [0,0], color='Red')\n",
    "ax.text(u[0]-0.5,u[1]+0.1,r'${\\bf u}$',size=20)\n",
    "ax.text(A.dot(u)[0]-0.7,A.dot(u)[1]+0.3,r'$A{\\bf u}$',size=20)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "For a \"typical\" vector (like $\\vu$) the action of $A$ is to scale, reflect, and/or rotate it.  \n",
    "\n",
    "But for some special vectors (like $\\vv$) the action of $A$ is only to \"stretch\" it (without any rotation or reflection).\n",
    "\n",
    "In fact, $A\\vv$ is simply $2\\vv.$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Today we will by studying equations such as \n",
    "\n",
    "$$ A\\vx = 2\\vx\\;\\;\\;\\;\\mbox{or}\\;\\;\\;\\;A\\vx = -4\\vx$$\n",
    "\n",
    "where special vectors are transformed by $A$ into scalar multiples of themselves."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "__Definition.__  \n",
    "\n",
    "An __eigenvector__ of an $n\\times n$ matrix $A$ is a nonzero vector $\\vx$ such that $A\\vx = \\lambda\\vx$ for some scalar $\\lambda.$  \n",
    "\n",
    "A scalar $\\lambda$ is called an __eigenvalue__ of $A$ if there is a nontrivial solution $\\vx$ of $A\\vx = \\lambda\\vx.$  \n",
    "\n",
    "Such an $\\vx$ is called an _eigenvector corresponding to $\\lambda.$_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Checking Eigenvectors and Eigenvalues"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Before considering how to compute eigenvectors, let's look at simply how to determine if a given vector is an eigenvector of a matrix."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Example.__  Let $A = \\mat{{rr}1&6\\\\5&2}, \\vu = \\mat{{r}6\\\\-5}, \\vv=\\mat{{r}3\\\\-2}.$  \n",
    "\n",
    "Are $\\vu$ and $\\vv$ eigenvectors of $A$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Solution.__\n",
    "\n",
    "$$A\\vu = \\mat{{rr}1&6\\\\5&2}\\mat{{r}6\\\\-5} = \\mat{{r}-24\\\\20} = -4\\mat{{r}6\\\\-5} = -4\\vu.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$A\\vv = \\mat{{rr}1&6\\\\5&2}\\mat{{r}3\\\\-2} = \\mat{{r}-9\\\\11} \\neq \\lambda\\mat{{r}3\\\\-2}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "So $\\vu$ is an eigenvector corresponding to the eigenvalue $-4$, but $\\vv$ is not an eigenvector of $A$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "__Example.__   Show that 7 is an eigenvalue of the matrix $A$, and find the corresponding eigenvectors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "For 7 to be an eigenvalue of $A$, it must be the case that \n",
    "\n",
    "$$ A\\vx=7\\vx$$\n",
    "\n",
    "has a nontrivial solution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This is equivalent to:\n",
    "\n",
    "$$ A\\vx - 7\\vx = {\\bf 0}$$\n",
    "\n",
    "or \n",
    "\n",
    "$$ (A - 7I)\\vx = {\\bf 0}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "To solve this homogeneous equation, form the matrix\n",
    "\n",
    "$$A - 7I = \\mat{{rr}1&6\\\\5&2}-\\mat{{rr}7&0\\\\0&7} = \\mat{{rr}-6&6\\\\5&-5}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The columns of $A-7I$ are obviously linearly dependent, so $(A - 7I)\\vx = {\\bf 0}$ has a nontrivial solution.\n",
    "\n",
    "So 7 is an eigenvalue of $A$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "To find the corresponding eigenvectors, we solve $(A - 7I)\\vx = {\\bf 0}$ using row operations:\n",
    "\n",
    "$$\\mat{{rrr}-6&6&0\\\\5&-5&0}\\sim\\mat{{rrr}1&-1&0\\\\0&0&0}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This says that $x_1 = x_2,$ and $x_2$ is free.\n",
    "\n",
    "So the general solution has the form $x_2\\mat{{r}1\\\\1}.$  Each vector of this form with $x_2 \\neq 0$ is an eigenvector corresponding to $\\lambda = 7.$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Question TIme! Q16.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Eigenspace"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Clearly, $\\lambda$ is an eigenvalue of an $n\\times n$ matrix $A$ if and only if the equation\n",
    "\n",
    "$$(A-\\lambda I)\\vx = {\\bf 0}$$\n",
    "\n",
    "has a nontrivial solution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Notice that the set of _all_ solutions of that equation is just _the null space of the matrix $A-\\lambda I.$_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "So the set of all eigenvectors corresponding to a particular $\\lambda$ is a _subspace of $\\R^n$_ and is called the __eigenspace__ of $A$ corresponding to $\\lambda$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Example.__  For matrix $A = \\mat{{rr}1&6\\\\5&2},$ we found that the general solution for the eigenvector corrsponding to $\\lambda = 7$ is the expression $\\vx_1\\mat{{r}1\\\\1}.$  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This means that the eigenspace corresponding to $\\lambda = 7$ consists of all multiples of $\\mat{{r}1\\\\1},$ which is the line through $(1,1)$ and the origin."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We could also show that the eigenspace corresponding to $\\lambda = -4$ is the line through $(-6,5)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
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    "slideshow": {
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NkhYskNzMhwcAAAAA4OJ5yZI0Vzix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      "text/plain": [
       "<matplotlib.figure.Figure at 0x113808cc0>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 470,
       "width": 699
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "ax = ut.plotSetup(-10,10,-6,10,size=(12,8))\n",
    "ut.centerAxes(ax)\n",
    "A = np.array([[1,6],[5,2]])\n",
    "u = np.array([1,1])\n",
    "v = np.array([3./2,-5./4])\n",
    "#\n",
    "ax.plot(v[0],v[1],'bo')\n",
    "ax.plot(A.dot(v)[0],A.dot(v)[1],'bo')\n",
    "ax.text(v[0],v[1]+0.2,r'${\\bf v}$',size=20)\n",
    "ax.text(A.dot(v)[0]+0.2,A.dot(v)[1]+0.2,r'$A{\\bf v}$',size=20)\n",
    "ax.plot([-10,10],[5*10/6.0,-5*10/6.0],'b-',lw=2)\n",
    "#\n",
    "ax.plot(u[0],u[1],'ro')\n",
    "ax.plot(A.dot(u)[0],A.dot(u)[1],'ro')\n",
    "ax.text(u[0]+0.7,u[1],r'${\\bf u}$',size=20)\n",
    "ax.text(A.dot(u)[0]+0.7,A.dot(u)[1],r'$A{\\bf u}$',size=20)\n",
    "ax.plot([-6,10],[-6,10],'r-',lw=2)\n",
    "# \n",
    "ax.annotate('', xy=(A.dot(u)[0], A.dot(u)[1]),  xycoords='data',\n",
    "                xytext=(u[0], u[1]), textcoords='data',\n",
    "                size=18,\n",
    "                #bbox=dict(boxstyle=\"round\", fc=\"0.8\"),\n",
    "                arrowprops={'arrowstyle': 'simple',\n",
    "                                'fc': '0.5', \n",
    "                                'ec': 'none',\n",
    "                                'connectionstyle' : 'arc3,rad=0.5'},\n",
    "                )\n",
    "ax.annotate('', xy=(A.dot(v)[0], A.dot(v)[1]),  xycoords='data',\n",
    "                xytext=(v[0], v[1]), textcoords='data',\n",
    "                size=18,\n",
    "                #bbox=dict(boxstyle=\"round\", fc=\"0.8\"),\n",
    "                arrowprops={'arrowstyle': 'simple',\n",
    "                                'fc': '0.5', \n",
    "                                'ec': 'none',\n",
    "                                'connectionstyle' : 'arc3,rad=-0.5'},\n",
    "                )\n",
    "ax.text(3,9,r'Eigenspace for $\\lambda$ = 7',size=16)\n",
    "ax.text(-9.5,8,r'Eigenspace for $\\lambda = -4$',size=16)\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "__Example.__  Let $A = \\mat{{rrr}4&-1&6\\\\2&1&6\\\\2&-1&8}.$  An eigenvalue of $A$ is $2.$  Find a basis for the the corresponding eigenspace."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Solution.__  The eigenspace we are looking for is the nullspace of $A - 2I.$  \n",
    "\n",
    "We will use the strategy for finding a basis for a nullspace that we learned in the last lecture."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Form\n",
    "\n",
    "$$A - 2I = \\mat{{rrr}4&-1&6\\\\2&1&6\\\\2&-1&8}-\\mat{{rrr}2&0&0\\\\0&2&0\\\\0&0&2} = \\mat{{rrr}2&-1&6\\\\2&-1&6\\\\2&-1&6}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "and row reduce the augmented matrix for $(A-2I)\\vx={\\bf 0}$:\n",
    "\n",
    "$$\\mat{{rrrr}2&-1&6&0\\\\2&-1&6&0\\\\2&-1&6&0} \\sim \\mat{{rrrr}2&-1&6&0\\\\0&0&0&0\\\\0&0&0&0}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "At this point, it is clear that 2 is indeed an eigenvalue of $A$ because the equation $(A-2I)\\vx = {\\bf 0}$ has free variables.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The general solution is $x_1 = \\frac{1}{2}x_2 +-3x_3.$\n",
    "\n",
    "Expressed as a vector, the general solution is:\n",
    "\n",
    "$$\\mat{{c}\\frac{1}{2}x_2 - 3x_3\\\\x_2\\\\x_3}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Expressed as a vector sum, this is:\n",
    "\n",
    "$$x_2\\mat{{c}1/2\\\\1\\\\0} + x_3\\mat{{r}-3\\\\0\\\\1}\\;\\;\\;\\;\\mbox{with $x_2$ and $x_3$ free.}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "So this eigenspace is a two-dimensional subspace of $\\R^3,$ and a basis for this subspace is\n",
    "\n",
    "$$\\left\\{\\mat{{c}1/2\\\\1\\\\0},\\mat{{r}-3\\\\0\\\\1}\\right\\}.$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    <script type=\"text/javascript\">\n",
       "        $(function(){\n",
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       "            if (p.length==0) return;\n",
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     "metadata": {},
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      "\n"
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WZemVV15p5cEJwW15dYuq68Jrp11mRdf8+3OdTnoBANVGdF0uuubnq2W/iioj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p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\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6c+aMcnNz9fXXX+vTTz/VVVddpf79+2v+/Pnq1q2b3eUBAAAAAFoYOlcBAO2aaZpyOBwq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\nAD74D+tdSdu4Hiz+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11358eeb8>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 460,
       "width": 683
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sl.hide_code_in_slideshow()\n",
    "ax = ut.plotSetup3d(-3,3,-3,3,-3,3,figsize=(12,8))\n",
    "v = np.array([1.,2.,0])\n",
    "v = v/np.sqrt(np.sum(v*v))\n",
    "u = np.array([-3.0,0,1.0])\n",
    "u = u/np.sqrt(np.sum(u*u))\n",
    "w = -v-2.0*u\n",
    "w = w/np.sqrt(np.sum(w*w))\n",
    "pts = np.array([v,u,w])\n",
    "#ax.text(v[0],v[1],v[2],r'$\\bf v$',size=20)\n",
    "#ax.text(u[0],u[1],u[2],r'$\\bf u$',size=20)\n",
    "ax.text(-2,-2,-3,r'Eigenspace for $\\lambda=2$',size=20)\n",
    "#ax.text(0.2,0.2,-4,r'$\\bf 0$',size=20)\n",
    "# plotting the span of v\n",
    "ut.plotSpan3d(ax,u,v,'Green')\n",
    "ut.plotPoint3d(ax,u[0],u[1],u[2],'r')\n",
    "ut.plotPoint3d(ax,v[0],v[1],v[2],'r')\n",
    "ut.plotPoint3d(ax,w[0],w[1],w[2],'r')\n",
    "ut.plotPoint3d(ax,0,0,0,'k')\n",
    "plt.quiver(pts[:,0],pts[:,1],pts[:,2],pts[:,0],pts[:,1],pts[:,2],length=1.0,color='Red',lw=2)\n",
    "pts = 2.0*pts\n",
    "plt.quiver(pts[:,0],pts[:,1],pts[:,2],pts[:,0],pts[:,1],pts[:,2],length=1.0,color='Blue',lw=2)\n",
    "u = 2*u\n",
    "v = 2*v\n",
    "w = 2*w\n",
    "ut.plotPoint3d(ax,u[0],u[1],u[2],'b')\n",
    "ut.plotPoint3d(ax,v[0],v[1],v[2],'b')\n",
    "ut.plotPoint3d(ax,w[0],w[1],w[2],'b')\n",
    "# plotting the axes\n",
    "# ut.plotIntersection3d(ax,[0,0,1,0],[0,1,0,0])\n",
    "# ut.plotIntersection3d(ax,[0,0,1,0],[1,0,0,0])\n",
    "ut.plotIntersection3d(ax,[0,1,0,0],[1,0,0,0])\n",
    "print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Question Time! Q16.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Eigenvalues of a Triangular Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Theorem.__  The eigenvalues of a triangular matrix are the entries on its main diagonal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Proof.__  We'll consider the $3\\times 3$ case.  If $A$ is upper triangular, then $A-\\lambda I$ has the form\n",
    "\n",
    "$$A - \\lambda I = \\mat{{rrr}a_{11}&a_{12}&a_{13}\\\\0&a_{22}&a_{23}\\\\0&0&a_{33}} - \\mat{{rrr}\\lambda&0&0\\\\0&\\lambda&0\\\\0&0&\\lambda}$$\n",
    "\n",
    "$$ = \\mat{{ccc}a_{11}-\\lambda&a_{12}&a_{13}\\\\0&a_{22}-\\lambda&a_{23}\\\\0&0&a_{33}-\\lambda}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Now, $\\lambda$ is an eigenvalue of $A$ if and only if the equation $(A-\\lambda I)\\vx = {\\bf 0}$ has a nontrivial solution -- in other words, if an only if the equation has a free variable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The special pattern that the zero entries have in $A$ means that there will be a free variable if any diagonal entry is also zero, because then there will be a column without a pivot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "That is, $(A-\\lambda I)\\vx = {\\bf 0}$ has a free variable if and only if at least one of the entries on the diagonal of $(A-\\lambda I)$ is zero."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This happens if and only if $\\lambda$ equals one of the entries $a_{11}, a_{22},$ or $a_{33}$ on the diagonal of $A$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "__Example.__  Let $A = \\mat{{rrr}3&6&-8\\\\0&0&6\\\\0&0&2}$ and $B = \\mat{{rrr}4&0&0\\\\-2&1&0\\\\5&3&4}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Then the eigenvalues of $A$ are 3, 0, and 2.   The eigenvalues of $B$ are 4 and 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Invertibility and Eigenvalues"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "So far we haven't probed what it means for a matrix to have an eigenvalue of 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This happens if and only if the equation $A\\vx = 0\\vx$ has a nontrivial solution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "But that equation is equivalent to $A\\vx = {\\bf 0}$ which has a nontrivial solution if and only if $A$ is not invertible."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This means that _0 is an eigenvalue of $A$ if and only if $A$ is not invertible._"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This draws an important connection between invertibility and zero eigenvalues."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "So we have __yet another__ addition to the Invertible Matrix Theorem!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Question Time! Q16.3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Eigenvectors and Difference Equations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Let's return to the problem we considered at the outset: predicting future values of $\\vx_t$ (the number of CS majors of each class in year $t$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We modeled the future as $\\vx_{t+1} = A\\vx_t\\;\\;\\;(t = 0,1,2,\\dots).$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "A __solution__ of such an equation is an explicit description of $\\{\\vx_t\\}$ whose formula for each $\\vx_t$ does not depend directly on $A$ or on the preceding terms in the sequence other than the initial term $\\vx_0.$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The simplest way to build a solution is to take an eigenvector $\\vx_0$ and its corresponding eigenvalue $\\lambda$ and let \n",
    "$$ \\vx_t = \\lambda^t \\vx_0 \\;\\;\\;(t = 0,1,2,\\dots)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This sequence is a solution because \n",
    "$$A\\vx_t = A(\\lambda^t\\vx_0) = \\lambda^t(A\\vx_0) = \\lambda^k(\\lambda\\vx_0) = \\lambda^{t+1}\\vx_0 = \\vx_{t+1}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We can extend this to combinations of eigenvectors.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "If $A$ has two eigenvectors $\\vu$ and $\\vv$ corresponding to eigenvalues $\\lambda$ and $\\mu$,\n",
    "then another solution is \n",
    "\n",
    "$$ x_t = \\lambda^t\\vu + \\mu^t \\vv$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "To address the problem of predicting the CS major population, we assume that we can express the state vector $\\vx$ as a linear combination of eigenvectors $\\vu_1, \\vu_2, \\dots,\\vu_p$.  (In fact this is always possible.)  That is, \n",
    "\n",
    "$$\\vx_0 = a_1\\vu_1 + a_2\\vu_2+\\dots+a_p\\vu_p.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Then at time $t$, \n",
    "\n",
    "$$\\vx_t = \\lambda_1^ta_1\\vu_1 + \\lambda_2^ta_2\\vu_2 + \\dots + \\lambda_p^ta_p\\vu_p.$$\n",
    "\n",
    "Which gives us an explicit solution for the number of students in the major in any future year."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Note that the expression above is exponential in each of the $\\lambda_1,\\dots,\\lambda_p$.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The resulting value will be essentially determined by the largest $\\lambda_i$.   \n",
    "\n",
    "To see this, let's say that $\\lambda_1$ is the largest eigenvalue, and $\\lambda_2$ is the second largest.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Then the proportion of $\\vu_1$ to $\\vu_2$ contained in $\\vx_t$ will be given by $(\\lambda_1/\\lambda_2)^t$.   \n",
    "\n",
    "Since this ratio is larger than 1, the relative proportion of $\\vu_1$ will grow exponentially.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This shows the importance of the largest eigenvalue in the value of $\\vx_t$ for large $t$.  In the long run, $\\vx_t$ will be very close to $\\lambda_1^t\\vu_1.$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The largest eigenvalue shows the asymptotic rate of growth (or shrinkage) of the state vector $\\vx_t$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "For the matrix $A$ that describes CS major population growth, the largest eigenvalue is 1.19.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "In fact, the incoming class (fall 2015) shows an increase in stated interest in CS of about 20%!"
   ]
  }
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