{ "cells": [ { "cell_type": "raw", "metadata": {}, "source": [ "Content under Creative Commons Attribution license CC-BY 4.0, code under BSD 3-Clause License © 2019 Lorena A. Barba, Tingyu Wang" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The matrix is everywhere\n", "\n", "This is a classic quote that has nothing to do with our lesson here: \n", "> _\"The Matrix is everywhere, it is all around us, even now in this very room.\"_ (Morpheus)\n", "\n", "We just couldn't help making a quip about the 1999 film [The Matrix](https://en.wikipedia.org/wiki/The_Matrix)!\n", "\n", "In this lesson, we revisit the key idea that a matrix is a linear transformation, and expand on it with three more perspectives on what matrices are and do: a matrix transforms a circle to an ellipse; a matrix is a system of equations; and, a matrix is a change of basis. We then play with matrices in three-dimensional space, and introduce the important concept of _rank_ of a matrix.\n", "\n", "Let's begin by importing our favorite libraries of scientific Python. We also load our helper plotting functions, which are in the script `plot_helper.py`. Make sure you have downloaded that file, as shown in [Lesson 1](http://go.gwu.edu/engcomp4lesson1) of this module." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy\n", "%matplotlib inline\n", "from matplotlib import pyplot" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import sys\n", "sys.path.append('../scripts/')\n", "\n", "# Our helper, with the functions: \n", "# plot_vector, plot_linear_transformation, plot_linear_transformations\n", "from plot_helper import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A matrix is a linear transformation\n", "\n", "In the first lesson of this module, we saw that a matrix corresponds to a linear transformation. For example, the matrix \n", "$$A = \\begin{bmatrix} 1 & 1 \\\\ -1 & 1 \\end{bmatrix}$$\n", "\n", "via matrix-vector multiplication, will transform the unit vectors to its columns:\n", "\n", "$$\\begin{eqnarray}\n", "\\mathbf{i} &=& \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix} \\Rightarrow \\begin{bmatrix} 1 \\\\ -1 \\end{bmatrix} \\\\\n", "\\mathbf{j} &=& \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} \\Rightarrow \\begin{bmatrix} 1 \\\\ 1 \\end{bmatrix}\n", "\\end{eqnarray}$$\n", "\n", "Let's use our helper function `plot_linear_transformation()` to visualize what this matrix does to the unit vectors and a grid on the 2D plane:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "A = numpy.array([[1,1], [-1,1]])\n", "plot_linear_transformation(A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You see that the transformation $A$ is a 45-degree clockwise rotation, plus a scaling by a factor that stretched the vectors $\\mathbf{i}$ and $\\mathbf{j}$ (shown in green and red) into vectors of more length. \n", "How much is the scaling factor?\n", "\n", "To start, we'll create the basis vectors and the vectors where they land, $\\mathbf{a}$ and $\\mathbf{b}$, corresponding to the columns of $A$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "i = numpy.array([1,0])\n", "j = numpy.array([0,1])" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "a = numpy.array([1,-1])\n", "b = numpy.array([1, 1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can resort to geometry to compute the length of the vectors $\\mathbf{i}$ and (its transformation) $\\mathbf{a}$, and compare them. But first, a plot of the two vectors helps us visualize." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "vectors = [i, a]\n", "plot_vector(vectors)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For $\\mathbf{i}$, we already know the length: it's a unit vector for a reason! We can also see right on the plot that its length is $1.0$. In the case of $\\mathbf{a}$, we can imagine a right triangle where $\\mathbf{a}$ is the hypotenuse, and remember the Pythagorean theorem for its length, which we also call the **norm** of the vector:\n", "\n", "$$ ||\\mathbf{a}||= \\sqrt{1^2 + 1^2} = \\sqrt{2}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Definition:*\n", "\n", "> The **Euclidean norm** of a 2D vector, that is, its length (or magnitude) is: $||\\mathbf{x}||= \\sqrt{x^2 + y^2}$, where $(x,y)$ are its coordinates. This definition generalizes to any dimension by adding all squared components under the square root.\n", "\n", "The NumPy sub-package [`numpy.linalg`](https://numpy.org/doc/stable/reference/routines.linalg.html#module-numpy.linalg) contains many useful functions, including one to compute the norm of a vector (or matrix). Try it with $\\mathbf{i}$ and $\\mathbf{a}$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.0" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "numpy.linalg.norm(i)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.4142135623730951" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "numpy.linalg.norm(a)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.4142135623730951" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "numpy.sqrt(2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Happy? \n", "After the transformation, the two unit vectors got scaled by $\\sqrt{2}$, and each grid box in the transformed plot has a side length of $\\sqrt{2}$. \n", "\n", "Consider an arbitrary vector in the plane, $\\mathbf{x} = \\begin{bmatrix} x \\\\ y \\end{bmatrix}$.\n", "\n", "Through the matrix-vector multiplication $A\\mathbf{x}$, the vector lands on the transformed space onto the combination of the matrix columns scaled by the vector components:\n", "\n", "$$\n", " A\\mathbf{x} = x\\,\\mathbf{a} + y\\,\\mathbf{b}\n", "$$\n", "\n", "This transformation rotates the vector by 45 degrees clockwise, and scales its length by $\\sqrt{2}$.\n", "The reverse action would be to rotate the space 45 degrees counter-clockwise, then scale all vectors by $\\frac{1}{\\sqrt{2}}$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At the end of our previous lesson, we learned to compute the inverse of a matrix using the `numpy.linalg` sub-package of NumPy, and we made a plot of a transformation and its inverse with our helper functions. \n", "Let's see how that looks for $A$." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "A_inv = numpy.linalg.inv(A)\n", "plot_linear_transformations(A, A_inv)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Alright! Like we expected, the two transformations in sequence bring all vectors right back to where they started.\n", "This reflects that the matrix multiplication $A^{-1}A$ is equal to the identity matrix, $I$.\n", "\n", "*Note:*\n", "\n", "In the previous lesson, we used the command \n", "```Python\n", "from numpy.linalg import inv\n", "```\n", "
\n", "\n", "This creates a shortcut `inv()` to [`numpy.linalg.inv()`](https://numpy.org/doc/stable/reference/generated/numpy.linalg.inv.html#numpy.linalg.inv), to save us some typing. But all the functions of `numpy.linalg` are already available to us when we import NumPy, and this command is not necessary. It's just a convenience—and sometimes a matter of style: many Pythonistas like to say that \"explicit is better than implicit\" and type the long name, while others savagely try to cut down on typing." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's visualize the action of $A^{-1}$ (the inverse of $A$) on its own:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_linear_transformation(A_inv)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we expected, $A^{-1}$ corresponds to a rotation by 45 degrees to the left, and a scaling factor that shrank the unit vectors. By how much? Let's see." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0.5 -0.5]\n", " [ 0.5 0.5]]\n" ] } ], "source": [ "print(A_inv)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This matrix takes the unit vector $\\mathbf{i}$ to a vector with coordinates $(0.5, 0.5)$. Using the Pythagorean theorem for triangles, we get the new length of the vector as $\\sqrt{0.5^2+0.5^2}=\\frac{1}{\\sqrt{2}}$, as we expected.\n", "\n", "Knowing the relationship between a matrix and its underlying transformation, we could visualize the reverse transformation of $A$ and might have easily computed $A^{-1}$ by hand, in this case." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Exercise:*\n", "\n", "Create the following matrix as a NumPy array: \n", "$$B = \\begin{bmatrix} 1 & 1 \\\\ 0 & -1 \\end{bmatrix}$$\n", "\n", "Use our helper function to visualize what it does to the unit vectors and a grid of lines. Then compute its inverse using `numpy.linalg.inv()`, and visualize the two transformations in sequence. Finally, visualize what the inverse does on its own. _Notice anything special?_" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A matrix transforms a circle to an ellipse\n", "\n", "Let's play with the transformation corresponding to the matrix\n", "\n", "$$C = \\begin{bmatrix} 2 & 1 \\\\ 1 & 2 \\end{bmatrix}$$" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[2 1]\n", " [1 2]]\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "C = numpy.array([[2,1], [1,2]])\n", "print(C)\n", "plot_linear_transformation(C)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The unit vectors $\\mathbf{i}$ and $\\mathbf{j}$ land on the columns of $C$, which seems to rotate them toward each other and stretch them." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To visualize the effect of this matrix, let's plot a bunch of vectors of unit length, their heads together tracing a unit circle.\n", "We start by creating an array of angles for these vectors, which we want to go around the origin from $0$ to $2\\pi$." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "alpha = numpy.linspace(0, 2*numpy.pi, 41)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Each vector's coordinates will be the pair $(\\cos\\alpha, \\sin\\alpha)$, with $\\alpha$ taking all the angle values in our array.\n", "To achieve a list of coordinate pairs, we can use a wonderful Python built-in function called `zip()`. If you pass it two iterable arguments of the same length (like lists or arrays), it _zips_ them into pairs." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "vectors = list(zip(numpy.cos(alpha), numpy.sin(alpha)))" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_vector(vectors)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1.0, 0.0)" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vectors[0]" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([2., 1.])" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "C.dot(numpy.array(vectors[0]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "OK. The first vector in our set is the unit vector $\\mathbf{i}$, and like we knew already, it lands on the first column of $C$ by the transformation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We next apply the transformation to all the vectors in our set, using a `for` statement, and we plot the transformed vectors." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "newvectors = []\n", "for i in range(len(vectors)):\n", " newvectors.append(C.dot(numpy.array(vectors[i])))" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_vector(newvectors)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Neat! Our set of vectors whose coordinates traced a unit circle got transformed to trace an ellipse. \n", "It looks like the ellipse has its major axis along the 45-degree line. We can get an approximation to its semi-major and semi-minor axes by finding the longest and shortest vectors in this new set. \n", "We can use the `numpy.linalg.norm()` function for this." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "lengths = []\n", "for i in range(len(newvectors)):\n", " lengths.append(numpy.linalg.norm(newvectors[i]))" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.0\n" ] } ], "source": [ "semi_major = max(lengths)\n", "print(semi_major)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.0\n" ] } ], "source": [ "semi_minor = min(lengths)\n", "print(semi_minor)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at one of the vectors along the semi-major axis. Its magnitude (length) is $3.0$, and its direction is 45 degrees from the horizontal. This means its horizontal and vertical components are the same, and take the value:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.1213203435596424" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "semi_major/numpy.sqrt(2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we create a vector with these coordinates: call it $\\mathbf{u}_1$. Call the vector that landed there after the transformation $\\mathbf{v}_1$—in other words, $C\\,\\mathbf{v}_1 = \\mathbf{u}_1$. \n", "\n", "Imagine multiplying the equation above by $C^{-1}$ to get $\\mathbf{v}_1=C^{-1}\\mathbf{u}_1$. We're saying that if $\\mathbf{v}_1$ lands on $\\mathbf{u}_1$ via the transformation $C$, then $\\mathbf{u}_1$ lands on $\\mathbf{v}_1$ via the transformation $C^{-1}$.\n", "\n", "In the code below, we compute the inverse of $C$ and multiply it with $\\mathbf{u}_1$ to get $\\mathbf{v}_1$. Then we plot the two vectors together.\n" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[2.12132034 2.12132034]\n" ] } ], "source": [ "u1 = numpy.array([semi_major/numpy.sqrt(2), semi_major/numpy.sqrt(2)])\n", "print(u1)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "C_inv = numpy.linalg.inv(C)\n", "v1 = C_inv.dot(u1)\n", "plot_vector([u1,v1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Funny. The vector $\\mathbf{v}_1$ is transformed by the matrix $C$ into a scaled version of itself. In other words: $\\mathbf{u}_1 = s_1 \\mathbf{v}_1$, where $s_1$ is the scaling factor. So,\n", "\n", "$$C\\,\\mathbf{v}_1 = s_1 \\mathbf{v}_1$$\n", "\n", "Wow. The effect of the matrix on this vector is just to scale it. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's now look at one of the vectors along the semi-minor axis (we pick the one pointing right and down), and repeat this process." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0.70710678 -0.70710678]\n" ] } ], "source": [ "u2 = numpy.array([semi_minor/numpy.sqrt(2), -semi_minor/numpy.sqrt(2)])\n", "print(u2)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0.70710678 -0.70710678]\n" ] }, { "data": { "image/png": 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aIDmhBkhOqAGSE2qA5IQaIDmhBkhOqAGSE2qA5IQaIDmhBkhOqAGSE2qA5P4XSbekucPf0eQAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "v2 = C_inv.dot(u2)\n", "print(v2)\n", "plot_vector([u2,v2])" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9999999999999999" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "numpy.linalg.norm(u2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hmm. The effect of the matrix on the vector $\\mathbf{v}_2$ is _also_ just to scale it, and the scaling factor is $1$.\n", "\n", "\n", "The vectors $\\mathbf{v}_1$ and $\\mathbf{v}_2$ are aligned \"just right\" so the effect of the transformation $C$ is to only scale them. They are special. They are **eigenvectors** of $C$.\n", "\n", "Do notice that the matrix $C$ in our example is _symmetric_. This will prove important, so we note it for future reference." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Key ideas:*\n", "\n", "> A 2D symmetric matrix transforms a unit circle to an ellipse on the plane.\n", "\n", "> A vector that doesn't change direction after a linear transformation is an _eigenvector_ of the matrix." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A matrix is a system of equations\n", "\n", "For any vector $\\mathbf{c}$ in the transformed space, can we find out what vector it came from before the transformation? That is, we'd like to find the vector $\\mathbf{x}$ such that \n", "\n", "$$ A\\mathbf{x}=\\mathbf{c} $$\n", "\n", "Take, for example, $\\mathbf{c} = \\begin{bmatrix} 1 \\\\ 5 \\end{bmatrix}$ and the components of $\\mathbf{x}$ as $(x, y)$. \n", "\n", "The vector $\\mathbf{x}$ lands on $\\mathbf{c}$ via the transformation $A$—that is, via the matrix-vector multiplication, which means a linear combination of the columns of $A$ scaled by the components of $\\mathbf{x}$:\n", "\n", "$$A\\mathbf{x}= x \\begin{bmatrix} 1 \\\\ -1 \\end{bmatrix}+ y \\begin{bmatrix} 1 \\\\ 1 \\end{bmatrix} = \\begin{bmatrix} 1 \\\\ 5 \\end{bmatrix}$$\n", "\n", "(Using the matrix $A$ defined at the beginning of this lesson.) We're asking to find the scalars in a linear combination of the column vectors $\\mathbf{a}$ and $\\mathbf{b}$ that gives $\\mathbf{c}$.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Writing this vector equation component-wise, we get two equations for the components $x$ and $y$:\n", "\n", "$$\n", "\\begin{align*}\n", "x + y &= 1 \\\\\n", "-x + y &= 5\n", "\\end{align*}\n", "$$\n", "\n", "So, the question we are asking is answered by solving a system of two linear equations, for two unknowns! " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We already know how to answer it by means of the inverse linear transformation, via the matrix-vector multiplication $A^{-1}\\mathbf{c}$. We can do this in NumPy:" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-2. 3.]\n" ] } ], "source": [ "c = numpy.array([1,5])\n", "x = A_inv.dot(c)\n", "print(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The vector $\\mathbf{x}$ is the **solution** of the linear system of equations. Look at the two linear equations again… we can isolate $y$ in each case, to re-write them as equations for lines in 2D space, i.e., in the form $y=mx+b$:\n", "\n", "\n", "$$\n", "\\begin{align*}\n", "y &= 1 - x\\\\\n", "y &= 5 + x\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To visualize these two lines, let's define an array of $x$-values, and then plot a line with each of these equations. We also add a marker at the point corresponding to the coordinates of the vector $\\mathbf{x}$." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xvalues = numpy.linspace(-4,2)\n", "m1, b1, m2, b2 = -1, 1, 1, 5\n", "\n", "pyplot.figure(figsize=(2,2))\n", "pyplot.plot(xvalues, m1*xvalues+b1)\n", "pyplot.plot(xvalues, m2*xvalues+b2)\n", "pyplot.scatter(x[0],x[1], s=5)\n", "pyplot.box(False)\n", "pyplot.grid(True);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You see that the coordinates of the solution vector $\\mathbf{x}$ are right at the intersection of the two lines that correspond to the equations in the linear system. Indeed, the point $(-2,3)$ belongs to both lines, and satisfies both linear equations.\n", "\n", "From this perspective, we look at the linear system row-by-row, and interpret each as a line in 2D space. It may even be a more familiar perspective to you. But it's less helpful when you start to think about systems of more dimensions!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "NumPy also has a built-in function to solve a linear system of equations: [`numpy.linalg.solve()`](https://numpy.org/doc/stable/reference/generated/numpy.linalg.solve.html#numpy.linalg.solve)—we give it the matrix, and the known vector on the right-hand side of the equation:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-2. 3.]\n" ] } ], "source": [ "x = numpy.linalg.solve(A, c)\n", "print(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suppose that we now want to solve a linear system with coefficient matrix $D$,\n", "\n", "$$D = \\begin{bmatrix} -2 & -1 \\\\ 1 & 0.5 \\end{bmatrix}$$\n", "\n", "Let's define this matrix as a NumPy array, and then visualize the transformation." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-2. -1. ]\n", " [ 1. 0.5]]\n" ] } ], "source": [ "D = numpy.array([[-2,-1], [1,0.5]])\n", "print(D)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_linear_transformation(D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Yikes! That's not good. We encountered this in the previous lesson, when we plotted 30 vectors made as (random) linear combinations of the column vectors:\n", "\n", "$$\n", " \\mathbf{a} = \\left[ \\begin{array}{c} -2 \\\\ 1 \\end{array} \\right], \\quad\n", " \\mathbf{d} = \\left[ \\begin{array}{c} -1 \\\\ 0.5 \\end{array} \\right] \n", "$$\n", "\n", "These two vectors are co-linear, i.e., their span is just a line.\n", "If you tried to obtain the inverse of $D$ using `numpy.linalg.inv(D)`, you will see the error message:\n", "```Python\n", "LinAlgError: Singular matrix\n", "```\n", "\n", "And if you try to solve the linear system with `numpy.linalg.solve(D, c)`, you will see the same error message.\n", "We can try to figure out what is happening using the row-by-row perspective, by which the two line equations are: \n", "\n", "$$\n", "\\begin{align*}\n", "y &= -1 - 2x\\\\\n", "y &= (5 - x)/0.5\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the two lines to see what is going on." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xvalues = numpy.linspace(-4,10)\n", "m1, b1, m2, b2 = -2, -1, -2, 10\n", "\n", "pyplot.figure(figsize=(2,2))\n", "pyplot.plot(xvalues, m1*xvalues+b1)\n", "pyplot.plot(xvalues, m2*xvalues+b2)\n", "pyplot.box(False)\n", "pyplot.grid(True);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The two lines are parallel and they thus never intersect: the system has no solution, or is **inconsistent**. \n", "\n", "If the right-hand-side vector were _itself_ colinear with the column vectors of $D$, then the system would have infinite solutions (the two equations are the same), or be **underdetermined**.\n", "For example, with the following right-hand-side vector\n", "$$\n", " \\left[ \\begin{array}{c} -4 \\\\ 2 \\end{array} \\right]\n", "$$\n", "the linear system, row-by-row, is\n", "$$\n", "\\begin{align*}\n", "-2x -1y &= -4 \\\\\n", "1x + 0.5y &= 2\n", "\\end{align*}\n", "$$\n", "You can see that the first equation is the same as the second equation multiplied by $-2$, and it adds no new information. \n", "The single equation, viewed as a transformation, takes a 2D vector as input, and gives a scalar as output. What is the matrix? \n", "Think about the left-hand side, $1x+0.5y$, as a linear combination of two matrix columns, scaled by the vector components: the column vectors are 1D, in this case, and the matrix is _non-square_:\n", "\n", "$$\\begin{bmatrix} 1 & 0.5 \\end{bmatrix} \\begin{bmatrix} x \\\\ y \\end{bmatrix} = 2\n", "$$\n", "\n", "We will discuss non-square matrices in Lesson 4. The key idea is that they represent transformations _between dimensions_ (in this case, from 2D to 1D)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A matrix is a change of basis\n", "\n", "We discussed _basis vectors_ in the previous lesson. Typically, we visualize the 2D plane as a grid of horizontal and vertical lines and use the unit vectors as basis:\n", "\n", "$$\n", "\\mathbf{i} = \\begin{bmatrix} 1 \\\\ 0 \\end{bmatrix}, \\quad\n", "\\mathbf{j} = \\begin{bmatrix} 0 \\\\ 1 \\end{bmatrix} \n", "$$\n", "\n", "This is the _standard basis_. But the definition of a basis allows us to choose any two _linearly independent_ vectors that span the 2D space. \n", "Why would you choose a different set of basis vectors? \n", "It could be that choosing a different basis makes a particular problem easier to solve.\n", "\n", "All the vectors in the plane can be written as a linear combination of the basis vectors. That power is what makes them a basis in the first place!\n", "\n", "Take the vector $\\mathbf{x} = \\begin{bmatrix} x \\\\ y \\end{bmatrix}$. It is equal to $x\\,\\mathbf{i}+y\\,\\mathbf{j}$.\n", "\n", "*Definition:*\n", "\n", "> A vector's **coordinates** are the scalars in the linear combination of the basis vectors that express that vector." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suppose we need to express the vector $\\mathbf{v}= \\begin{bmatrix} -3 \\\\ 0 \\end{bmatrix}$ as a linear combination of\n", "\n", "$$\n", "\\mathbf{a} = \\begin{bmatrix} 2 \\\\ 1 \\end{bmatrix}, \\quad\n", "\\mathbf{b} = \\begin{bmatrix} 1 \\\\ 2 \\end{bmatrix} \n", "$$\n", "\n", "These are the vectors that form the column of our matrix $C$ from the previous section." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[2 1]\n", " [1 2]]\n" ] } ], "source": [ "print(C)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the standard basis, the vector's coordinates are $(-3, 0)$. We're asking what its coordinates would be if we used $\\mathbf{a}$ and $\\mathbf{b}$ as basis vectors. \n", "Given that matrix multiplication is a linear combination of the matrix columns scaled by the vector coordinates, we're asking to find $\\mathbf{x}$ such that\n", "\n", "$$ C\\mathbf{x}=\\mathbf{v} $$\n", "\n", "Well, that amounts to solving a linear system. Here is the solution:" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-2. 1.]\n" ] } ], "source": [ "v = numpy.array([-3,0])\n", "x = numpy.linalg.solve(C, v)\n", "print(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The vector $\\mathbf{v}$ has coordinates $(-2,1)$ in the new basis $\\mathbf{a}$ and $\\mathbf{b}$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's visualize the change of basis from $\\mathbf{i}$ and $\\mathbf{j}$ to $\\mathbf{a}$ and $\\mathbf{b}$, and see how the same vector $\\mathbf{v}$ is represented by different bases. Here we use our custom plotting function `plot_change_basis()` which takes the new basis vectors' coordinates in the standard basis as arguments." ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "a = numpy.array([2,1])\n", "b = numpy.array([1,2])\n", "plot_change_basis(a, b, v)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On the left plot, $\\mathbf{v}$ is represented by $-3\\,\\mathbf{i}+0\\,\\mathbf{j}$, so it has coordinates $(-3,0)$ in the standard basis. \n", "\n", "On the right plot, the same vector $\\mathbf{v}$ is represented by $-2\\,\\mathbf{a}+1\\,\\mathbf{b}$, so it has coordinates $(-2,1)$ in the new basis, which verifies our result using `numpy.linalg.solve`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Key idea:*\n", "\n", "> The matrix $C$ formed with the new basis vectors as columns is the matrix that converts from the coordinate system using that basis, to the standard basis.\n", "\n", "Going the other way around, from the standard basis to the new basis, we need to multiply by $C^{-1}$. That's why we had to _solve_ $ C\\mathbf{x}=\\mathbf{v} $ above to get the coordinates on the new basis of the vector $\\mathbf{v}$.\n", "\n", "What if we wanted to apply a known transformation to some vector expressed in the new basis? We have the matrix that represents the transformation in the standard basis. For example, consider the 90-degree rotation, $R$:\n", "$$ R = \\begin{bmatrix} 0 & -1 \\\\\n", " 1 & 0 \\end{bmatrix} $$\n", "\n", "We would need to first change the representation of the vector to the standard basis (multiplying by $C$), then apply the transformation, then change back to the new basis—we need $C^{-1}R\\, C \\,\\mathbf{x}$.\n", "\n", "*Note:*\n", "\n", "Not _all_ matrices are a change of basis. Remember that a basis is a set of linearly independent vectors that span the space. To be a change of basis, a matrix needs to have linearly independent columns.\n", "\n", "If you need a bit more help understanding change of basis, we recommend episode 12 of the wonderful series [_\"Essence of Linear Algebra\"_](http://3b1b.co/eola) [1]." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Think:*\n", "\n", "> As a linear transformation, a matrix transforms a vector to a new vector under the same basis. As a change of basis, a matrix can express the same vector's coordinates in a new coordinate system (new basis).\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Matrices in three-dimensional space\n", "\n", "The ideas of a matrix as a linear transformation, as a linear system of equations, or as a change of basis apply in any dimension. As for the idea that a matrix transforms a circle to an ellipse, it generalizes to transforming a sphere to an ellipsoid—in any dimension! It is easier to _visualize_ what is going on in two dimensions, so we begin there and establish the foundations. \n", "\n", "Let's now make the jump to the third dimension! You could start by watching the short episode 5 of _\"Essence of Linear Algebra\"_ [2].\n", "\n", "To explore 3D transformations, we'll take advantage of interactive figures in JupyterLab (or Notebook 7, the new version of Jupyter Notebook as of 2023), which we obtain using the `%matplotlib widget` command. (This requires that the [`ipympl`](https://matplotlib.org/ipympl/) package is available, and you may need to install it if it's not.)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "%matplotlib widget" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Linear transformations in 3D\n", "\n", "We'll use a helper function, `plot_3d_linear_transformation()`, which takes a $3\\times 3$ matrix, and draws a set of grid lines in perspective, before and after the transformation. \n", "\n", "Let's try it with this matrix:\n", "\n", "$M = \\begin{bmatrix}\n", " 1 & 0 & 1 \\\\\n", " 1 & 1 & 0 \\\\\n", " -1 & 1 & 1\n", " \\end{bmatrix} $\n", "\n", "Notice, again, that we create the matrix as a NumPy array with a list of rows." ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 1 0 1]\n", " [ 1 1 0]\n", " [-1 1 1]]\n" ] } ], "source": [ "M = numpy.array([[1,0,1], [1,1,0], [-1,1,1]])\n", "print(M)" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "d516b52483a44af2afeaeef4aeeab055", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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But the idea of a transformation as a matrix-vector multiplication, and in turn as a linear combination of the matrix columns, is the same.\n", "\n", "Let's consider the multiplication of $M$ with a 3D vector $\\mathbf{x}=\\begin{bmatrix}\n", " x \\\\\n", " y \\\\\n", " z \\end{bmatrix}$\n", "\n", "$$\n", " M \\mathbf{x} = x \\, \\begin{bmatrix}1 \\\\ 1 \\\\-1 \\end{bmatrix}+\n", " y \\, \\begin{bmatrix}0 \\\\ 1 \\\\ 1 \\end{bmatrix}+\n", " z \\, \\begin{bmatrix}1 \\\\ 0 \\\\ 1 \\end{bmatrix}\n", "$$\n", "\n", "The transformation will take the unit vector $\\mathbf{i}$, which in 3D has coordinates $(1, 0, 0)$ to the first column of the matrix. We can make a mental effort (or draw a picture) to imagine that the vector rotates around the $z$ axis to touch with its head the grid plane $y=1$, then rotates downwards to $z=-1$. \n", "\n", "*Challenge:*\n", "> Make a sketch on a piece of paper of how each unit vector is transformed by $M$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3D systems of linear equations\n", "\n", "Suppose that we have a vector $\\mathbf{u}$ in the transformed space, and we want to find out the vector it came from in the original space. Just like in the 2D case, this question is answered by solving a linear system of equations.\n", "\n", "With the multiplication $M\\mathbf{x}$ written out element-wise, and taking the right-hand-side vector as $(-1, 0, 2)$, we have:\n", "\n", "\n", "$$\n", "\\begin{align*}\n", "x + z &= -1 \\\\\n", "x + y &= 0 \\\\\n", "-x + y + z &= 2\n", "\\end{align*}\n", "$$\n", "\n", "We can solve this system using `numpy.linalg.solve()`, as before:" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-1. 1. 0.]\n" ] } ], "source": [ "u = numpy.array([-1, 0, 2])\n", "x = numpy.linalg.solve(M, u)\n", "print(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The matrix $M$ takes a vector $\\mathbf{x}$ with coordinates $(-1, 1, 0)$ and transforms it to a vector $\\mathbf{u}$ with coordinates $(-1, 0, 2)$.\n", "\n", "We can write the general system as $M\\mathbf{x} = \\mathbf{u}$, and sometimes say that $\\mathbf{x}$ is the _input vector_ and $\\mathbf{u}$ the _output vector_ of the transformation $M$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Dimension and rank\n", "\n", "Let's play with a different matrix:\n", "\n", "$N = \\begin{bmatrix}\n", " 1 & 2 & 7 \\\\\n", " 0 & 1 & 3 \\\\\n", " -3 & 1 & 0\n", " \\end{bmatrix} $\n", "\n", "The interactive mode of figures in Jupyter obtained with the `%matplotlib widget` magic lets us drag the 3D plot to view different camera angles. Go ahead and move around the plot of the grid after transformation via matrix $N$." ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 1 2 7]\n", " [ 0 1 3]\n", " [-3 1 0]]\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "be5f10ab72fd4ee1b6200e1e8fe0427d", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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We lost a dimension!\n", "\n", "What is going on here?\n", "\n", "Let's look at the system of equations $N\\,\\mathbf{x}= \\mathbf{0}$ (the zero vector), and write it out by rows:\n", "\n", "$$\n", "\\begin{align*}\n", " x + 2y + 7z &= 0 \\\\\n", " y + 3z &= 0 \\\\\n", "-3x + y &= 0\n", "\\end{align*}\n", "$$\n", "\n", "The last linear equation gives $y=3x$, which when plugged back in the first and second equations gives: $7x+7z=0$, and $3x+3z=0$. These two equations are the same! Pick any value of $z$, and you can pick $x=-z$ and $y=3x$ to satisfy the system—$z$ is a _free variable_." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*Definition:*\n", "\n", "> A linear system with a zero-vector on the right-hand side is called **homogeneous**. The set of all solutions to the homogeneous system $N\\,\\mathbf{x}= \\mathbf{0}$ is called the **nullspace** of $N$ (sometimes called \"kernel\").\n", "\n", "The nullspace of our matrix $N$ is all the scalings: \n", "$\\; z \\begin{bmatrix}\n", " -1 \\\\\n", " -3 \\\\\n", " 1 \\end{bmatrix}$.\n", "\n", "This is a line: a one-dimensional space. When the nullspace of a matrix has non-zero dimension (i.e., the zero vector is not its only solution), it means its columns are _linearly dependent_.\n", "\n", "Recall when we said that not all matrices can be a change of basis? To be a change of basis, its columns need to be linearly independent. In this case, the columns of $N$ are not a basis for 3D space—the space spanned by the columns of $N$ is a plane, i.e., it's two-dimensional.\n", "\n", "*Definition:*\n", "\n", "> The dimension of the column space of a matrix is called its **rank**.\n", "\n", "We can get the rank of a matrix with NumPy using the `numpy.linalg.matrix_rank()` function. Check it out:" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "numpy.linalg.matrix_rank(N)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our matrix $N$ is $3\\times3$—if its rank were $3$, we would say that it has _full rank_: its rank matches the number of columns. But the rank of $N$ is $2$, so we say that it's _rank deficient_ or _singular_. In the 2D case, a matrix with two linearly dependent columns has rank $1$, and transforms all vectors onto a line. \n", "\n", "Rank-deficient matrices reduce dimensionality and are called _projections_. They are useful in many applications, like architecture and computer graphics, where you can use them to cast shadows." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's now play with the matrix:\n", "\n", "$L = \\begin{bmatrix}\n", " 1 & 2 & 1 \\\\\n", " -1 & -2 & -1 \\\\\n", " 3 & 6 & 3\n", " \\end{bmatrix} $" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 1 2 1]\n", " [-1 -2 -1]\n", " [ 3 6 3]]\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "4c9ca3980ea54bfba4e69abc0e1a8294", "version_major": 2, "version_minor": 0 }, "image/png": 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", "text/html": [ "\n", "
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\n", " " ], "text/plain": [ "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "L = numpy.array([[1,2,1], [-1,-2,-1], [3,6,3]])\n", "print(L)\n", "plot_3d_linear_transformation(L)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you drag around our plot of the wireframe cube after the transformation, you see that it's just a line. In this case, the matrix takes every 3D vector to a one-dimensional space, because it has rank $1$." ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "numpy.linalg.matrix_rank(L)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Can we solve a system of equations if the system matrix is rank-deficient?\n", "\n", "The answer is no (in general). Imagine trying to find the inverse transformation that takes vectors from a plane (or a line) and builds back the 3D space. That's just not possible: the matrix inverse does not exist (we say the matrix is _not invertible_) when the matrix is not full rank." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What we've learned\n", "\n", "- How to compute the norm of a vector.\n", "- A 2D matrix transforms a unit circle into an ellipse.\n", "- The vectors that don't change direction after a linear transformation are eigenvectors of the matrix.\n", "- For any vector in the transformed space, find the vector it came from by solving $A\\mathbf{x}=\\mathbf{c}$ for $\\mathbf{x}$.\n", "- Look at the 2D linear system row-by-row and interpret each row as a line; the solution is the point of intersection.\n", "- Use `numpy.linalg.solve()` to get the solution vector.\n", "- In 2D, when the two rows of the linear system represent parallel lines, the system is inconsistent (no solution).\n", "- The vectors $\\mathbf{i}=(1,0)^T$ and $\\mathbf{j}=(0,1)^T$ are the standard basis in 2D.\n", "- Form a matrix $C$ with any pair of basis vectors as columns: it transforms vectors from the coordinate system using that basis to the standard basis. To tranform vectors from the standard basis to the new basis, multiply by $C^{-1}$.\n", "- Apply a known transformation $R$ by transforming to the standard basis first, then back: $C^{-1} R C\\mathbf{x}$.\n", "- A homogeneous linear system has the zero vector on the right-hand side.\n", "- The set of all solutions to the homogeneous system $N\\,\\mathbf{x}=\\mathbf{0}$ is the nullspace of N.\n", "- The rank of a matrix is the dimension of its column space." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "1. Change of basis. Essence of linear algebra, chapter 12. Video at https://youtu.be/P2LTAUO1TdA (2016), by Grant Sanderson.\n", "\n", "2. Three-dimensional linear transformations. Essence of linear algebra, chapter 5. Video at https://youtu.be/rHLEWRxRGiM (2016), by Grant Sanderson." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Execute this cell to load the notebook's style sheet, then ignore it\n", "from IPython.core.display import HTML\n", "css_file = '../../../styles/custom.css'\n", "HTML(open(css_file, \"r\").read())" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.5" } }, "nbformat": 4, "nbformat_minor": 4 }