{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9a126241-9672-4522-9675-dab49009ff74",
   "metadata": {},
   "source": [
    "# Matrix Math\n",
    "\n",
    "Our Notebooks are not meant to serve as a comprehensive recap of mathematics in general.  We're not engaged in the project of forming an encyclopedia.  Far from it.  The purpose of these Notebooks is more to demonstrate a methodolgy a teacher or student might adopt in order to give rise to (to float) a curriculum. \n",
    "\n",
    "A curriculum is a host of topics that hang together and mutually refer to one another, more like a mini-language or simple system.\n",
    "\n",
    "This Matrix Math page is a case in point.  The Pauli Matricies usually appear in the context of particle physics aka quantum mechanics, which features groups, such as SU(2) and SU(3).  That context is mentioned in the embedded Youtubes, but this Notebook itself is silent about the physics of whatsons (e.g. electrons) but for here.\n",
    "\n",
    "Many of our pages contain the word sandbox in their filenames, or otherwise remind that they're more like playgrounds, or one could say launch pads, or jumping off points, into wider studies.\n",
    "\n",
    "An individual curriculum developer and/or team will crystallize only so much content.  For example Stephen Wolfram and his brother Conrad likewise advocate, through demonstration, span mathematics with Mathematica and its Wolfram Language, another set of landscapes in a different ecosystem, not featuring the Python language.  \n",
    "\n",
    "For many students, a curriculum such as this one might serve as a stepping stone to the Wolfram universe. Tour in other lands, and return with baubles.  Take forth our Quadrays and Cabal of Polyhedrons to these other worlds, bring back skills and insights.\n",
    "\n",
    "One way to approach a math is to let its jargon pile up for awhile, as you keep exercising the jargon to make sure you have it down.  \n",
    "\n",
    "Spending too much time on one concept may actually be a pitfall, because it depends for its meaning on other concepts.  To delay reaching these other concepts is to make understanding even a first one all that more difficult.\n",
    "\n",
    "For example, the idea of a complex conjugate, of a number or matrix, as distinct from its inverse or transpose, may not at first be clear.  \n",
    "\n",
    "However, already, we know a matrix has an inverse and so on.  That could be the news right there.  Then we go back and add more flesh."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a7731214-fc91-441c-9544-17920816eb5c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import YouTubeVideo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0eab47fc-8d44-43b5-9fa4-b2f09d6666ea",
   "metadata": {},
   "outputs": [
    {
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      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x10fcf0250>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "YouTubeVideo(\"yeK2N7FbkVI\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "89aca6ef-e51c-4e7d-89ca-ac8ac4a5a6c3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/DUuTx2nbizM\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            \n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x11134b340>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "YouTubeVideo(\"DUuTx2nbizM\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9f15acc3-0e72-4922-9e35-8a572dfc603f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/7rE9gcj5I2U\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            \n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x11134b520>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "YouTubeVideo(\"7rE9gcj5I2U\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "072fb335-5940-4446-841d-bad4749f742a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/ganF52dxL1U\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            \n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x11134b700>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "YouTubeVideo(\"ganF52dxL1U\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "8041957f-9e78-46da-b92a-cc556961dcec",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "from sympy import Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63f89cbe-2c80-4e47-bc88-5e8c520cef6f",
   "metadata": {},
   "source": [
    "We're in the realm of $\\mathbb{C}$.\n",
    "\n",
    "* A Matrix is Hermitian if it equals its own conjugate transpose.\n",
    "* A Matrix is Skew Hermitian if its negative equals its conjugate transpose\n",
    "* A Matrix is Unitary if its inverse equals its conjugate transpose\n",
    "* A Matrix is Special Unitary if it is unitary and has a determinant of 1."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d85f6fc9-ef4a-4f6d-8249-a22357736b85",
   "metadata": {},
   "source": [
    "The Pauli Matrices are unitary and Hermitian, meaning they also have to be self inverses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5feec171-5114-4b1d-98d2-a3a67d2ed035",
   "metadata": {},
   "outputs": [],
   "source": [
    "σ0, σ1, σ2, σ3 = sp.symbols('σ0 σ1 σ2 σ3')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "797048d2-1f48-4a74-853b-6249277477bf",
   "metadata": {},
   "source": [
    "## Sandbox Area"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "404d9f89-82a0-47c5-9958-7411a41323d1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle i$"
      ],
      "text/plain": [
       "I"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.sqrt(-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8c65a8ab-be37-4327-86bc-3c55d80fc742",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle i$"
      ],
      "text/plain": [
       "I"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "64fd7bb8-d554-4483-9aef-6d6c0a740cab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - i$"
      ],
      "text/plain": [
       "-I"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.I.conjugate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "dec444cd-ef29-4da8-8861-cc33d9340e46",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 3 + 2 i$"
      ],
      "text/plain": [
       "3 + 2*I"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = 3 + 2*sp.I; c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9d72befe-a2d3-40b0-acbd-9281af7cde55",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 3 - 2 i$"
      ],
      "text/plain": [
       "3 - 2*I"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c.conjugate() # change the sign of the imaginary part"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f1ac60e5-f6d0-4889-9790-7074153af69a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left(3 - 2 i\\right) \\left(3 + 2 i\\right)$"
      ],
      "text/plain": [
       "(3 - 2*I)*(3 + 2*I)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c * c.conjugate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "0e4c88d0-90bc-4fbd-be98-ba09494d2db7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 13$"
      ],
      "text/plain": [
       "13"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "_.expand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "01ad0f0e-ac81-4501-bd01-850895bb2276",
   "metadata": {},
   "outputs": [],
   "source": [
    "a, b = sp.symbols('a b')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ca99685-eb13-4305-9180-d4d459244afd",
   "metadata": {},
   "source": [
    "Here are the four 2x2 Pauli matrices, including I itself as \"sigma zero\" (σ0)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "98d51b7e-746e-4322-9ad0-68cdc2c31ef0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 0\\\\0 & 1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1, 0],\n",
       "[0, 1]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "σ0 = sp.eye(2)\n",
    "σ0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "36b3ad60-12ae-41e1-87a8-574929f51ffd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0, 1],\n",
       "[1, 0]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "σ1 = Matrix([[0, 1], [1, 0]])\n",
    "σ1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "70d3203c-2721-4a06-8dc2-c044d9232018",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & - i\\\\i & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0, -I],\n",
       "[I,  0]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "σ2 = Matrix([[0, -sp.I], [sp.I, 0]])\n",
    "σ2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "c61ef2c8-1926-4fde-896a-1be423a30124",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 0\\\\0 & -1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1,  0],\n",
       "[0, -1]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "σ3 = Matrix([[1, 0], [0, -1]])\n",
    "σ3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5cf1859-f38c-4fcc-9ab8-06467928e445",
   "metadata": {},
   "source": [
    "That Pauli matrices self multiply to give an inverse is another way of saying they're self inverses.\n",
    "\n",
    "$$\n",
    "A A^{-1} = I\n",
    "$$\n",
    "\n",
    "$$\n",
    "A = 1/A\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "fbdbc18f-f1db-4e7a-a81e-b6ca83250be2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(Matrix([\n",
       " [1, 0],\n",
       " [0, 1]]),\n",
       " Matrix([\n",
       " [1, 0],\n",
       " [0, 1]]),\n",
       " Matrix([\n",
       " [1, 0],\n",
       " [0, 1]]),\n",
       " Matrix([\n",
       " [1, 0],\n",
       " [0, 1]]))"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "σ0 ** 2, σ1 ** 2, σ2 ** 2, σ3 ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "65c86ccc-c13b-433d-b844-44e0d6953f1f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & - i\\\\- i & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[ 0, -I],\n",
       "[-I,  0]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "σ3 * σ2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "7f88901c-41c8-4736-a180-164ef960c237",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & i\\\\i & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0, I],\n",
       "[I, 0]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "σ2 * σ3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "8be749ac-5962-4bd0-8024-fc38bb05e70b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & - 2 i\\\\- 2 i & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[   0, -2*I],\n",
       "[-2*I,    0]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "σ3 * σ2 - σ2 * σ3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "bea18187-d913-47c1-8f79-2cf33a682d8c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 2 i\\\\2 i & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  0, 2*I],\n",
       "[2*I,   0]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = 2 * sp.I * σ1; m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "5db3e732-ff07-4286-8aa6-08e69d4fc08b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & - 2 i\\\\- 2 i & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[   0, -2*I],\n",
       "[-2*I,    0]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.conjugate()  # change the sign of any imaginary part"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "e65c8906-87f3-4a6d-a546-128cd7d2f952",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & - 2 i\\\\- 2 i & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[   0, -2*I],\n",
       "[-2*I,    0]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m_h = m.conjugate().transpose()\n",
    "m_h"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c48f527-ed56-490d-bf89-8aebe7b080b0",
   "metadata": {},
   "source": [
    "\n",
    "* Hermitian: $A^{\\dagger} = A$\n",
    "* Unitary:  $A^{\\dagger} = A^{-1}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "aa1b6e90-6f89-45fe-ad84-82c604b57dbb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}4 & 0\\\\0 & 4\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[4, 0],\n",
       "[0, 4]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m * m_h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "f2e029b7-631f-4d4f-98cc-e308f22ee539",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & - \\frac{i}{2}\\\\- \\frac{i}{2} & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[   0, -I/2],\n",
       "[-I/2,    0]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.inv()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "89deb8bc-1800-4d97-9ad0-b78b8e1125a8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 0\\\\0 & 1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1, 0],\n",
       "[0, 1]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m * m.inv()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "adc0afda-37e4-42f7-8463-bbbecd15e6ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.is_hermitian  # complex conjugate is also the inverse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "184dd6b2-28dd-43cc-b5e9-e6b571a6eade",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "σ3.is_hermitian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "80fe7de0-433d-4d66-8913-37ed8bbeb627",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "σ3 == σ3.conjugate().transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "e501637b-5697-48a1-b054-ff3a3e6f2ece",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "σ2.is_hermitian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "41d92c18-9601-4159-a5ec-f9de67287c21",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "σ2.inv() == σ2.conjugate().transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "6cfe8998-182a-4f72-aaac-757a6d06104e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "σ1.is_hermitian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "d8958c74-5075-4d19-b88d-0fe2b3d884a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0, 1],\n",
       "[1, 0]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "σ1.inv()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "4467ece1-40e9-4b9f-a23c-7b2b014bd0af",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1 & 0\\\\0 & 1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[1, 0],\n",
       "[0, 1]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "σ1.inv() * σ1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "d715a471-1070-4ca7-ba61-e77ed2996606",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 1\\\\1 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0, 1],\n",
       "[1, 0]])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "σ1.conjugate().transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "a08ea317-1f14-4979-8b25-3c50900f1370",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle -1$"
      ],
      "text/plain": [
       "-1"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "σ1.det()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "eaf26677-f178-42a3-9d33-f606cab40cf9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle -1$"
      ],
      "text/plain": [
       "-1"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "σ2.det()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "9af28090-b112-462a-bf56-59d11e577871",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle -1$"
      ],
      "text/plain": [
       "-1"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "σ3.det()"
   ]
  }
 ],
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