2.3 Identity and Inverse Matrices.ipynb

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   "execution_count": 1,
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "# Plot parameters\n",
    "sns.set()\n",
    "%pylab inline\n",
    "pylab.rcParams['figure.figsize'] = (4, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Avoid inaccurate floating values (for inverse matrices in dot product for instance)\n",
    "# See https://stackoverflow.com/questions/24537791/numpy-matrix-inversion-rounding-errors\n",
    "np.set_printoptions(suppress=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction\n",
    "\n",
    "This chapter is light but contains some important definitions. The identity matrix or the inverse of a matrix are concepts that will be very useful in the next chapters. We will see at the end of this chapter that we can solve systems of linear equations by using the inverse matrix. So hang on!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2.3 Identity and Inverse Matrices\n",
    "\n",
    "\n",
    "# Identity matrices\n",
    "\n",
    "The identity matrix $\\bs{I}_n$ is a special matrix of shape ($n \\times n$) that is filled with $0$ except the diagonal that is filled with 1.\n",
    "\n",
    "<img src=\"images/identity-matrix.png\" width=\"150\" alt=\"Example of an identity matrix\" title=\"Identity matrix\">\n",
    "<em>A 3 by 3 identity matrix</em>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An identity matrix can be created with the Numpy function `eye()`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  0.,  0.],\n",
       "       [ 0.,  1.,  0.],\n",
       "       [ 0.,  0.,  1.]])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
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   "source": [
    "np.eye(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 0., 1.]])"
      ]
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     "execution_count": 5,
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   ],
   "source": [
    "np.identity(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When 'apply' the identity matrix to a vector the result is this same vector:\n",
    "\n",
    "$$\\bs{I}_n\\bs{x} = \\bs{x}$$\n",
    "\n",
    "### Example 1.\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "    1 & 0 & 0 \\\\\\\\\n",
    "    0 & 1 & 0 \\\\\\\\\n",
    "    0 & 0 & 1\n",
    "\\end{bmatrix}\n",
    "\\times\n",
    "\\begin{bmatrix}\n",
    "    x_{1} \\\\\\\\\n",
    "    x_{2} \\\\\\\\\n",
    "    x_{3}\n",
    "\\end{bmatrix}=\n",
    "\\begin{bmatrix}\n",
    "    1 \\times x_1 + 0 \\times x_2 + 0\\times x_3 \\\\\\\\\n",
    "    0 \\times x_1 + 1 \\times x_2 + 0\\times x_3 \\\\\\\\\n",
    "    0 \\times x_1 + 0 \\times x_2 + 1\\times x_3\n",
    "\\end{bmatrix}=\n",
    "\\begin{bmatrix}\n",
    "    x_{1} \\\\\\\\\n",
    "    x_{2} \\\\\\\\\n",
    "    x_{3}\n",
    "\\end{bmatrix}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2],\n",
       "       [6],\n",
       "       [3]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([[2], [6], [3]])\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 1)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
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   "source": [
    "x.shape"
   ]
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   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2.],\n",
       "       [6.],\n",
       "       [3.]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
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   ],
   "source": [
    "xid = np.eye(x.shape[0]).dot(x)\n",
    "xid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Intuition\n",
    "\n",
    "You can think of a matrix as a way to transform objects in a $n$-dimensional space. It applies a linear transformation of the space. We can say that we *apply* a matrix to an element: this means that we do the dot product between this matrix and the element (more details about the dot product in [2.2](https://hadrienj.github.io/posts/Deep-Learning-Book-Series-2.2-Multiplying-Matrices-and-Vectors/)). We will see this notion thoroughly in the next chapters but the identity matrix is a good first example. It is a particular example because the space doesn't change when we *apply* the identity matrix to it.\n",
    "\n",
    "<span class='pquote'>\n",
    "    The space doesn't change when we *apply* the identity matrix to it\n",
    "</span>\n",
    "\n",
    "We saw that $\\bs{x}$ was not altered after being multiplied by $\\bs{I}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Inverse Matrices\n",
    "\n",
    "The matrix inverse of $\\bs{A}$ is denoted $\\bs{A}^{-1}$. It is the matrix that results in the identity matrix when it is multiplied by $\\bs{A}$:\n",
    "\n",
    "$$\\bs{A}^{-1}\\bs{A}=\\bs{I}_n$$\n",
    "\n",
    "This means that if we apply a linear transformation to the space with $\\bs{A}$, it is possible to go back with $\\bs{A}^{-1}$. It provides a way to cancel the transformation.\n",
    "\n",
    "### Example 2.\n",
    "\n",
    "$$\n",
    "\\bs{A}=\\begin{bmatrix}\n",
    "    3 & 0 & 2 \\\\\\\\\n",
    "    2 & 0 & -2 \\\\\\\\\n",
    "    0 & 1 & 1\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "For this example, we will use the Numpy function `linalg.inv()` to calculate the inverse of $\\bs{A}$. Let's start by creating $\\bs{A}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3,  0,  2],\n",
       "       [ 2,  0, -2],\n",
       "       [ 0,  1,  1]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[3, 0, 2], [2, 0, -2], [0, 1, 1]])\n",
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we calculate its inverse:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.2,  0.2,  0. ],\n",
       "       [-0.2,  0.3,  1. ],\n",
       "       [ 0.2, -0.3, -0. ]])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_inv = np.linalg.inv(A)\n",
    "A_inv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can check that $\\bs{A_{inv}}$ is well the inverse of $\\bs{A}$ with Python:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  0., -0.],\n",
       "       [ 0.,  1., -0.],\n",
       "       [ 0.,  0.,  1.]])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_bis = A_inv.dot(A)\n",
    "A_bis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will see that inverse of matrices can be very usefull, for instance to solve a set of linear equations. We must note however that non square matrices (matrices with more columns than rows or more rows than columns) don't have inverse."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sovling a system of linear equations\n",
    "\n",
    "An introduction on system of linear equations.\n",
    "\n",
    "The inverse matrix can be used to solve the equation $\\bs{Ax}=\\bs{b}$ by adding it to each term:\n",
    "\n",
    "$$\\bs{A}^{-1}\\bs{Ax}=\\bs{A}^{-1}\\bs{b}$$\n",
    "\n",
    "Since we know by definition that $\\bs{A}^{-1}\\bs{A}=\\bs{I}$, we have:\n",
    "\n",
    "$$\\bs{I}_n\\bs{x}=\\bs{A}^{-1}\\bs{b}$$\n",
    "\n",
    "We saw that a vector is not changed when multiplied by the identity matrix. So we can write:\n",
    "\n",
    "$$\\bs{x}=\\bs{A}^{-1}\\bs{b}$$\n",
    "\n",
    "This is great! We can solve a set of linear equation just by computing the inverse of $\\bs{A}$ and apply this matrix to the vector of results $\\bs{b}$!\n",
    "\n",
    "Let's try that!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Write a Code and Shif+Enter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example 3.\n",
    "\n",
    "We will take a simple solvable example:\n",
    "\n",
    "$$\n",
    "\\begin{cases}\n",
    "y = 2x \\\\\\\\\n",
    "y = -x +3\n",
    "\\end{cases}\n",
    "$$\n",
    "\n",
    "We will use the notation that :\n",
    "\n",
    "$$\n",
    "\\begin{cases}\n",
    "A_{1,1}x_1 + A_{1,2}x_2 = b_1 \\\\\\\\\n",
    "A_{2,1}x_1 + A_{2,2}x_2= b_2\n",
    "\\end{cases}\n",
    "$$\n",
    "\n",
    "Here, $x_1$ corresponds to $x$ and $x_2$ corresponds to $y$. So we have:\n",
    "\n",
    "$$\n",
    "\\begin{cases}\n",
    "2x_1 - x_2 = 0 \\\\\\\\\n",
    "x_1 + x_2= 3\n",
    "\\end{cases}\n",
    "$$\n",
    "\n",
    "Our matrix $\\bs{A}$ of weights is:\n",
    "\n",
    "$$\n",
    "\\bs{A}=\n",
    "\\begin{bmatrix}\n",
    "    2 & -1 \\\\\\\\\n",
    "    1 & 1\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "And the vector $\\bs{b}$ containing the solutions of individual equations is:\n",
    "\n",
    "$$\n",
    "\\bs{b}=\n",
    "\\begin{bmatrix}\n",
    "    0 \\\\\\\\\n",
    "    3\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "Under the matrix form, our systems becomes:\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix}\n",
    "    2 & -1 \\\\\\\\\n",
    "    1 & 1\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "    x_1 \\\\\\\\\n",
    "    x_2\n",
    "\\end{bmatrix}=\n",
    "\\begin{bmatrix}\n",
    "    0 \\\\\\\\\n",
    "    3\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "Let's find the inverse of $\\bs{A}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2, -1],\n",
       "       [ 1,  1]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[2, -1], [1, 1]])\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.33333333,  0.33333333],\n",
       "       [-0.33333333,  0.66666667]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A_inv = np.linalg.inv(A)\n",
    "A_inv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have also:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "b = np.array([[0], [3]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since we saw that\n",
    "\n",
    "$$\\bs{x}=\\bs{A}^{-1}\\bs{b}$$\n",
    "\n",
    "We have:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.],\n",
       "       [2.]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = A_inv.dot(b)\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is our solution! \n",
    "\n",
    "$$\n",
    "\\bs{x}=\n",
    "\\begin{bmatrix}\n",
    "    1 \\\\\\\\\n",
    "    2\n",
    "\\end{bmatrix}\n",
    "$$\n",
    "\n",
    "This means that the point of coordinates (1, 2) is the solution and is at the intersection of the lines representing the equations. Let's plot them to check this solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 2160x1080 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(-10, 10)\n",
    "y = 2*x\n",
    "y1 = -x + 3\n",
    "\n",
    "plt.figure(figsize=(30,15))  # Size of Ouput\n",
    "plt.plot(x, y)  # 2D line plot\n",
    "plt.plot(x, y1)\n",
    "plt.xlim(0, 3)  # limites of X  axis\n",
    "plt.ylim(0, 3)  # limites of y axis\n",
    "# draw axes\n",
    "plt.axvline(x=0, color='grey')  # axis Vertical Line\n",
    "plt.axhline(y=0, color='grey')  # axis horzintal line\n",
    "plt.show() # display the Image\n",
    "plt.close() # Close Plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the solution (corresponding to the line crossing) is when $x=1$ and $y=2$. It confirms what we found with the matrix inversion!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Write a Code and Shif+Enter \n",
    "# Plot all Q from above fig by change limites of x and y "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## BONUS: Coding tip - Draw an equation\n",
    "\n",
    "To draw the equation with Matplotlib, we first need to create a vector with all the $x$ values. Actually, since this is a line, only two points would have been sufficient. But with more complex functions, the length of the vector $x$ corresponds to the sampling rate. So here we used the Numpy function `arrange()` (see the [doc](https://docs.scipy.org/doc/numpy/reference/generated/numpy.arange.html)) to create a vector from $-10$ to $10$ (not included)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-10,  -9,  -8,  -7,  -6,  -5,  -4,  -3,  -2,  -1,   0,   1,   2,\n",
       "         3,   4,   5,   6,   7,   8,   9])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(-10, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first argument is the starting point and the second the ending point. You can add a third argument to specify the step:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-10,  -8,  -6,  -4,  -2,   0,   2,   4,   6,   8])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(-10, 10, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we create a second vector $y$ that depends on the $x$ vector. Numpy will take each value of $x$ and apply the equation formula to it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-19, -17, -15, -13, -11,  -9,  -7,  -5,  -3,  -1,   1,   3,   5,\n",
       "         7,   9,  11,  13,  15,  17,  19])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(-10, 10)\n",
    "y = 2*x + 1\n",
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, you just need to plot these vectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x206252730f0>]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2160x1080 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Write a Code and Shif+Enter\n",
    "plt.figure(figsize=(30,15))\n",
    "plt.plot(x,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Singular matrices\n",
    "\n",
    "Some matrices are not invertible. They are called **singular**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion\n",
    "\n",
    "This introduces different cases according to the linear system because $\\bs{A}^{-1}$ exists only if the equation $\\bs{Ax}=\\bs{b}$ has one and only one solution.is almost all about systems of linear equations and number of solutions."
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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 },
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}