ortho-diag.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Math 3410: Orthogonal Diagonalization Example\n",
    "\n",
    "Consider the following matrix:\n",
    "\n",
    "$$A = \\begin{bmatrix}3&5&-1&1\\\\5&3&1&-1\\\\-1&1&3&5\\\\1&-1&5&3\\end{bmatrix}$$\n",
    "\n",
    "(This is an exercise from Nicholson -- notice the block form: $A = \\begin{bmatrix}A_1&A_2\\\\A_2&A_1\\end{bmatrix}$)\n",
    "\n",
    "Let's find the eigenvalues:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "hidden": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\lambda \\left(\\lambda - 8\\right)^{2} \\left(\\lambda + 4\\right)$"
      ],
      "text/plain": [
       "         2        \n",
       "λ⋅(λ - 8) ⋅(λ + 4)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "init_printing()\n",
    "A = Matrix([[3,5,-1,1],[5,3,1,-1],[-1,1,3,5],[1,-1,5,3]])\n",
    "factor(A.charpoly().as_expr())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": false
   },
   "source": [
    "The eigenvalues are $-4, 0$, and $8$ (which has multiplicity 2). Let's get the eigenvectors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "hidden": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[ \\left( -4, \\  1, \\  \\left[ \\left[\\begin{matrix}-1\\\\1\\\\-1\\\\1\\end{matrix}\\right]\\right]\\right), \\  \\left( 0, \\  1, \\  \\left[ \\left[\\begin{matrix}1\\\\-1\\\\-1\\\\1\\end{matrix}\\right]\\right]\\right), \\  \\left( 8, \\  2, \\  \\left[ \\left[\\begin{matrix}1\\\\1\\\\0\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0\\\\0\\\\1\\\\1\\end{matrix}\\right]\\right]\\right)\\right]$"
      ],
      "text/plain": [
       "⎡⎛       ⎡⎡-1⎤⎤⎞  ⎛      ⎡⎡1 ⎤⎤⎞  ⎛      ⎡⎡1⎤  ⎡0⎤⎤⎞⎤\n",
       "⎢⎜       ⎢⎢  ⎥⎥⎟  ⎜      ⎢⎢  ⎥⎥⎟  ⎜      ⎢⎢ ⎥  ⎢ ⎥⎥⎟⎥\n",
       "⎢⎜       ⎢⎢1 ⎥⎥⎟  ⎜      ⎢⎢-1⎥⎥⎟  ⎜      ⎢⎢1⎥  ⎢0⎥⎥⎟⎥\n",
       "⎢⎜-4, 1, ⎢⎢  ⎥⎥⎟, ⎜0, 1, ⎢⎢  ⎥⎥⎟, ⎜8, 2, ⎢⎢ ⎥, ⎢ ⎥⎥⎟⎥\n",
       "⎢⎜       ⎢⎢-1⎥⎥⎟  ⎜      ⎢⎢-1⎥⎥⎟  ⎜      ⎢⎢0⎥  ⎢1⎥⎥⎟⎥\n",
       "⎢⎜       ⎢⎢  ⎥⎥⎟  ⎜      ⎢⎢  ⎥⎥⎟  ⎜      ⎢⎢ ⎥  ⎢ ⎥⎥⎟⎥\n",
       "⎣⎝       ⎣⎣1 ⎦⎦⎠  ⎝      ⎣⎣1 ⎦⎦⎠  ⎝      ⎣⎣0⎦  ⎣1⎦⎦⎠⎦"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L=A.eigenvects()\n",
    "L"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": false
   },
   "source": [
    "Our eigenvectors are:\n",
    "\n",
    "$X = \\begin{bmatrix}-1\\\\1\\\\-1\\\\1\\end{bmatrix}$, corresponding to $\\lambda =-4$, \n",
    "$Y = \\begin{bmatrix}1\\\\-1\\\\-1\\\\1\\end{bmatrix}$, corresponding to $\\lambda = 0$,\n",
    "$Z_1 = \\begin{bmatrix}1\\\\1\\\\0\\\\0\\end{bmatrix}$ and $Z_2 = \\begin{bmatrix}0\\\\0\\\\1\\\\1\\end{bmatrix}$, corresponding to $\\lambda=8$.\n",
    "\n",
    "Notice that $X$ is orthogonal to $Y, Z_1, Z_2$, $Y$ is orthogonal to $Z_1, Z_2$ (and $X$, of course). This much is guaranteed.\n",
    "\n",
    "We also see that $Z_1$ is orthogonal to $Z_2$, which is **not** guaranteed - we got lucky! Ordinarily, for repeated eigenvalues we have to use the Gram Schmidt algorithm to produce an orthogonal basis for the corresponding eigenspace."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "hidden": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( \\left[\\begin{matrix}-1\\\\1\\\\-1\\\\1\\end{matrix}\\right], \\  \\left[\\begin{matrix}1\\\\-1\\\\-1\\\\1\\end{matrix}\\right], \\  \\left[\\begin{matrix}1\\\\1\\\\0\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0\\\\0\\\\1\\\\1\\end{matrix}\\right]\\right)$"
      ],
      "text/plain": [
       "⎛⎡-1⎤  ⎡1 ⎤  ⎡1⎤  ⎡0⎤⎞\n",
       "⎜⎢  ⎥  ⎢  ⎥  ⎢ ⎥  ⎢ ⎥⎟\n",
       "⎜⎢1 ⎥  ⎢-1⎥  ⎢1⎥  ⎢0⎥⎟\n",
       "⎜⎢  ⎥, ⎢  ⎥, ⎢ ⎥, ⎢ ⎥⎟\n",
       "⎜⎢-1⎥  ⎢-1⎥  ⎢0⎥  ⎢1⎥⎟\n",
       "⎜⎢  ⎥  ⎢  ⎥  ⎢ ⎥  ⎢ ⎥⎟\n",
       "⎝⎣1 ⎦  ⎣1 ⎦  ⎣0⎦  ⎣1⎦⎠"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = L[0][2][0]\n",
    "Y = L[1][2][0]\n",
    "Z1= L[2][2][0]\n",
    "Z2= L[2][2][1]\n",
    "EV=X,Y,Z1,Z2\n",
    "EV"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": false
   },
   "source": [
    "In caes you want confirmation that these are eigenvectors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "hidden": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left( \\left[\\begin{matrix}4\\\\-4\\\\4\\\\-4\\end{matrix}\\right], \\  \\left[\\begin{matrix}0\\\\0\\\\0\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}8\\\\8\\\\0\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0\\\\0\\\\8\\\\8\\end{matrix}\\right]\\right)$"
      ],
      "text/plain": [
       "⎛⎡4 ⎤  ⎡0⎤  ⎡8⎤  ⎡0⎤⎞\n",
       "⎜⎢  ⎥  ⎢ ⎥  ⎢ ⎥  ⎢ ⎥⎟\n",
       "⎜⎢-4⎥  ⎢0⎥  ⎢8⎥  ⎢0⎥⎟\n",
       "⎜⎢  ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥⎟\n",
       "⎜⎢4 ⎥  ⎢0⎥  ⎢0⎥  ⎢8⎥⎟\n",
       "⎜⎢  ⎥  ⎢ ⎥  ⎢ ⎥  ⎢ ⎥⎟\n",
       "⎝⎣-4⎦  ⎣0⎦  ⎣0⎦  ⎣8⎦⎠"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A*X, A*Y, A*Z1, A*Z2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": false
   },
   "source": [
    "Or, more efficiently:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "hidden": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ \\left[\\begin{matrix}4\\\\-4\\\\4\\\\-4\\end{matrix}\\right], \\  \\left[\\begin{matrix}0\\\\0\\\\0\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}8\\\\8\\\\0\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0\\\\0\\\\8\\\\8\\end{matrix}\\right]\\right]$"
      ],
      "text/plain": [
       "⎡⎡4 ⎤  ⎡0⎤  ⎡8⎤  ⎡0⎤⎤\n",
       "⎢⎢  ⎥  ⎢ ⎥  ⎢ ⎥  ⎢ ⎥⎥\n",
       "⎢⎢-4⎥  ⎢0⎥  ⎢8⎥  ⎢0⎥⎥\n",
       "⎢⎢  ⎥, ⎢ ⎥, ⎢ ⎥, ⎢ ⎥⎥\n",
       "⎢⎢4 ⎥  ⎢0⎥  ⎢0⎥  ⎢8⎥⎥\n",
       "⎢⎢  ⎥  ⎢ ⎥  ⎢ ⎥  ⎢ ⎥⎥\n",
       "⎣⎣-4⎦  ⎣0⎦  ⎣0⎦  ⎣8⎦⎦"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigen_check = list()\n",
    "for i in range(4):\n",
    "    eigen_check.append(A*EV[i])\n",
    "eigen_check"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": false
   },
   "source": [
    "Notice that any linear combination of $Z_1$ and $Z_2$ is again an eigenvector for $\\lambda=8$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "hidden": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( \\left[\\begin{matrix}x\\\\x\\\\y\\\\y\\end{matrix}\\right], \\  \\left[\\begin{matrix}8 x\\\\8 x\\\\8 y\\\\8 y\\end{matrix}\\right]\\right)$"
      ],
      "text/plain": [
       "⎛⎡x⎤  ⎡8⋅x⎤⎞\n",
       "⎜⎢ ⎥  ⎢   ⎥⎟\n",
       "⎜⎢x⎥  ⎢8⋅x⎥⎟\n",
       "⎜⎢ ⎥, ⎢   ⎥⎟\n",
       "⎜⎢y⎥  ⎢8⋅y⎥⎟\n",
       "⎜⎢ ⎥  ⎢   ⎥⎟\n",
       "⎝⎣y⎦  ⎣8⋅y⎦⎠"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x,y=symbols('x,y')\n",
    "Z = x*Z1+y*Z2\n",
    "Z,A*Z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": false
   },
   "source": [
    "Next, we diagonalize. The matrix $P$ is formed by normalizing our eigenvectors, and writing them as columns in a matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "hidden": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[ \\left[\\begin{matrix}- \\frac{1}{2}\\\\\\frac{1}{2}\\\\- \\frac{1}{2}\\\\\\frac{1}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{1}{2}\\\\- \\frac{1}{2}\\\\- \\frac{1}{2}\\\\\\frac{1}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}\\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2}\\\\0\\\\0\\end{matrix}\\right], \\  \\left[\\begin{matrix}0\\\\0\\\\\\frac{\\sqrt{2}}{2}\\\\\\frac{\\sqrt{2}}{2}\\end{matrix}\\right]\\right]$"
      ],
      "text/plain": [
       "⎡                ⎡√2⎤  ⎡0 ⎤⎤\n",
       "⎢                ⎢──⎥  ⎢  ⎥⎥\n",
       "⎢⎡-1/2⎤  ⎡1/2 ⎤  ⎢2 ⎥  ⎢0 ⎥⎥\n",
       "⎢⎢    ⎥  ⎢    ⎥  ⎢  ⎥  ⎢  ⎥⎥\n",
       "⎢⎢1/2 ⎥  ⎢-1/2⎥  ⎢√2⎥  ⎢√2⎥⎥\n",
       "⎢⎢    ⎥, ⎢    ⎥, ⎢──⎥, ⎢──⎥⎥\n",
       "⎢⎢-1/2⎥  ⎢-1/2⎥  ⎢2 ⎥  ⎢2 ⎥⎥\n",
       "⎢⎢    ⎥  ⎢    ⎥  ⎢  ⎥  ⎢  ⎥⎥\n",
       "⎢⎣1/2 ⎦  ⎣1/2 ⎦  ⎢0 ⎥  ⎢√2⎥⎥\n",
       "⎢                ⎢  ⎥  ⎢──⎥⎥\n",
       "⎣                ⎣0 ⎦  ⎣2 ⎦⎦"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigen_onb = list()\n",
    "for i in range(4):\n",
    "    eigen_onb.append((1/EV[i].norm())*EV[i])\n",
    "eigen_onb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "hidden": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left( \\left[\\begin{matrix}- \\frac{1}{2} & \\frac{1}{2} & \\frac{\\sqrt{2}}{2} & 0\\\\\\frac{1}{2} & - \\frac{1}{2} & \\frac{\\sqrt{2}}{2} & 0\\\\- \\frac{1}{2} & - \\frac{1}{2} & 0 & \\frac{\\sqrt{2}}{2}\\\\\\frac{1}{2} & \\frac{1}{2} & 0 & \\frac{\\sqrt{2}}{2}\\end{matrix}\\right], \\  \\left[\\begin{matrix}1 & 0 & 0 & 0\\\\0 & 1 & 0 & 0\\\\0 & 0 & 1 & 0\\\\0 & 0 & 0 & 1\\end{matrix}\\right]\\right)$"
      ],
      "text/plain": [
       "⎛⎡            √2    ⎤              ⎞\n",
       "⎜⎢-1/2  1/2   ──  0 ⎥              ⎟\n",
       "⎜⎢            2     ⎥              ⎟\n",
       "⎜⎢                  ⎥              ⎟\n",
       "⎜⎢            √2    ⎥  ⎡1  0  0  0⎤⎟\n",
       "⎜⎢1/2   -1/2  ──  0 ⎥  ⎢          ⎥⎟\n",
       "⎜⎢            2     ⎥  ⎢0  1  0  0⎥⎟\n",
       "⎜⎢                  ⎥, ⎢          ⎥⎟\n",
       "⎜⎢                √2⎥  ⎢0  0  1  0⎥⎟\n",
       "⎜⎢-1/2  -1/2  0   ──⎥  ⎢          ⎥⎟\n",
       "⎜⎢                2 ⎥  ⎣0  0  0  1⎦⎟\n",
       "⎜⎢                  ⎥              ⎟\n",
       "⎜⎢                √2⎥              ⎟\n",
       "⎜⎢1/2   1/2   0   ──⎥              ⎟\n",
       "⎝⎣                2 ⎦              ⎠"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P = Matrix(BlockMatrix(eigen_onb))\n",
    "P,P*P.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": false
   },
   "source": [
    "Now we can diagonalize. Notice that since $P$ is orthogonal, $P^T=P^{-1}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "hidden": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}-4 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 8 & 0\\\\0 & 0 & 0 & 8\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡-4  0  0  0⎤\n",
       "⎢           ⎥\n",
       "⎢0   0  0  0⎥\n",
       "⎢           ⎥\n",
       "⎢0   0  8  0⎥\n",
       "⎢           ⎥\n",
       "⎣0   0  0  8⎦"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D=(P.T)*A*P\n",
    "D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": false
   },
   "source": [
    "One thing diagonalization is good for is efficiently computing powers of matrices:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "hidden": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}9394170331095332911557922387157348107735883130854895153245866385385917584630949876979177035417468610835120128 & 9394170331095332911557922387157348111269577260411663812412461386871754616285917670730414951660681013420359680 & -1766847064778384329583297500742918515827483896875618958121606201292619776 & 1766847064778384329583297500742918515827483896875618958121606201292619776\\\\9394170331095332911557922387157348111269577260411663812412461386871754616285917670730414951660681013420359680 & 9394170331095332911557922387157348107735883130854895153245866385385917584630949876979177035417468610835120128 & 1766847064778384329583297500742918515827483896875618958121606201292619776 & -1766847064778384329583297500742918515827483896875618958121606201292619776\\\\-1766847064778384329583297500742918515827483896875618958121606201292619776 & 1766847064778384329583297500742918515827483896875618958121606201292619776 & 9394170331095332911557922387157348107735883130854895153245866385385917584630949876979177035417468610835120128 & 9394170331095332911557922387157348111269577260411663812412461386871754616285917670730414951660681013420359680\\\\1766847064778384329583297500742918515827483896875618958121606201292619776 & -1766847064778384329583297500742918515827483896875618958121606201292619776 & 9394170331095332911557922387157348111269577260411663812412461386871754616285917670730414951660681013420359680 & 9394170331095332911557922387157348107735883130854895153245866385385917584630949876979177035417468610835120128\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡93941703310953329115579223871573481077358831308548951532458663853859175846309\n",
       "⎢                                                                             \n",
       "⎢93941703310953329115579223871573481112695772604116638124124613868717546162859\n",
       "⎢                                                                             \n",
       "⎢                 -17668470647783843295832975007429185158274838968756189581216\n",
       "⎢                                                                             \n",
       "⎣                  17668470647783843295832975007429185158274838968756189581216\n",
       "\n",
       "49876979177035417468610835120128  93941703310953329115579223871573481112695772\n",
       "                                                                              \n",
       "17670730414951660681013420359680  93941703310953329115579223871573481077358831\n",
       "                                                                              \n",
       "06201292619776                                      17668470647783843295832975\n",
       "                                                                              \n",
       "06201292619776                                     -17668470647783843295832975\n",
       "\n",
       "60411663812412461386871754616285917670730414951660681013420359680             \n",
       "                                                                              \n",
       "30854895153245866385385917584630949876979177035417468610835120128             \n",
       "                                                                              \n",
       "00742918515827483896875618958121606201292619776                    93941703310\n",
       "                                                                              \n",
       "00742918515827483896875618958121606201292619776                    93941703310\n",
       "\n",
       "      -17668470647783843295832975007429185158274838968756189581216062012926197\n",
       "                                                                              \n",
       "       17668470647783843295832975007429185158274838968756189581216062012926197\n",
       "                                                                              \n",
       "953329115579223871573481077358831308548951532458663853859175846309498769791770\n",
       "                                                                              \n",
       "953329115579223871573481112695772604116638124124613868717546162859176707304149\n",
       "\n",
       "76                                      17668470647783843295832975007429185158\n",
       "                                                                              \n",
       "76                                     -17668470647783843295832975007429185158\n",
       "                                                                              \n",
       "35417468610835120128  93941703310953329115579223871573481112695772604116638124\n",
       "                                                                              \n",
       "51660681013420359680  93941703310953329115579223871573481077358831308548951532\n",
       "\n",
       "27483896875618958121606201292619776                  ⎤\n",
       "                                                     ⎥\n",
       "27483896875618958121606201292619776                  ⎥\n",
       "                                                     ⎥\n",
       "12461386871754616285917670730414951660681013420359680⎥\n",
       "                                                     ⎥\n",
       "45866385385917584630949876979177035417468610835120128⎦"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A**121"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "hidden": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}9394170331095332911557922387157348107735883130854895153245866385385917584630949876979177035417468610835120128 & 9394170331095332911557922387157348111269577260411663812412461386871754616285917670730414951660681013420359680 & -1766847064778384329583297500742918515827483896875618958121606201292619776 & 1766847064778384329583297500742918515827483896875618958121606201292619776\\\\9394170331095332911557922387157348111269577260411663812412461386871754616285917670730414951660681013420359680 & 9394170331095332911557922387157348107735883130854895153245866385385917584630949876979177035417468610835120128 & 1766847064778384329583297500742918515827483896875618958121606201292619776 & -1766847064778384329583297500742918515827483896875618958121606201292619776\\\\-1766847064778384329583297500742918515827483896875618958121606201292619776 & 1766847064778384329583297500742918515827483896875618958121606201292619776 & 9394170331095332911557922387157348107735883130854895153245866385385917584630949876979177035417468610835120128 & 9394170331095332911557922387157348111269577260411663812412461386871754616285917670730414951660681013420359680\\\\1766847064778384329583297500742918515827483896875618958121606201292619776 & -1766847064778384329583297500742918515827483896875618958121606201292619776 & 9394170331095332911557922387157348111269577260411663812412461386871754616285917670730414951660681013420359680 & 9394170331095332911557922387157348107735883130854895153245866385385917584630949876979177035417468610835120128\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡93941703310953329115579223871573481077358831308548951532458663853859175846309\n",
       "⎢                                                                             \n",
       "⎢93941703310953329115579223871573481112695772604116638124124613868717546162859\n",
       "⎢                                                                             \n",
       "⎢                 -17668470647783843295832975007429185158274838968756189581216\n",
       "⎢                                                                             \n",
       "⎣                  17668470647783843295832975007429185158274838968756189581216\n",
       "\n",
       "49876979177035417468610835120128  93941703310953329115579223871573481112695772\n",
       "                                                                              \n",
       "17670730414951660681013420359680  93941703310953329115579223871573481077358831\n",
       "                                                                              \n",
       "06201292619776                                      17668470647783843295832975\n",
       "                                                                              \n",
       "06201292619776                                     -17668470647783843295832975\n",
       "\n",
       "60411663812412461386871754616285917670730414951660681013420359680             \n",
       "                                                                              \n",
       "30854895153245866385385917584630949876979177035417468610835120128             \n",
       "                                                                              \n",
       "00742918515827483896875618958121606201292619776                    93941703310\n",
       "                                                                              \n",
       "00742918515827483896875618958121606201292619776                    93941703310\n",
       "\n",
       "      -17668470647783843295832975007429185158274838968756189581216062012926197\n",
       "                                                                              \n",
       "       17668470647783843295832975007429185158274838968756189581216062012926197\n",
       "                                                                              \n",
       "953329115579223871573481077358831308548951532458663853859175846309498769791770\n",
       "                                                                              \n",
       "953329115579223871573481112695772604116638124124613868717546162859176707304149\n",
       "\n",
       "76                                      17668470647783843295832975007429185158\n",
       "                                                                              \n",
       "76                                     -17668470647783843295832975007429185158\n",
       "                                                                              \n",
       "35417468610835120128  93941703310953329115579223871573481112695772604116638124\n",
       "                                                                              \n",
       "51660681013420359680  93941703310953329115579223871573481077358831308548951532\n",
       "\n",
       "27483896875618958121606201292619776                  ⎤\n",
       "                                                     ⎥\n",
       "27483896875618958121606201292619776                  ⎥\n",
       "                                                     ⎥\n",
       "12461386871754616285917670730414951660681013420359680⎥\n",
       "                                                     ⎥\n",
       "45866385385917584630949876979177035417468610835120128⎦"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P*(D**121)*P.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": false
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}