Matrices

matrices.ipynb

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      "source": "import sympy as sym\nimport numpy as np\nfrom IPython.display import display,Math",
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      "source": "def disp(expr):\n    display(Math(sym.latex(sym.sympify(expr))))",
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      "source": "A = np.array([[1,2], [3,4]])\ndisp(A)",
      "execution_count": 8,
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        {
          "data": {
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 2\\\\3 & 4\\end{matrix}\\right]$",
            "text/plain": "<IPython.core.display.Math object>"
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      "cell_type": "code",
      "source": "mat = np.zeros([4,6])\ndisp(mat)\nmat[0,1] = 2\ndisp(mat)",
      "execution_count": 11,
      "outputs": [
        {
          "data": {
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\end{matrix}\\right]$",
            "text/plain": "<IPython.core.display.Math object>"
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          "metadata": {},
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        {
          "data": {
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}0.0 & 2.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\end{matrix}\\right]$",
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      "cell_type": "code",
      "source": "numrange = range(0,4)\nmat = np.zeros([4,6])\nfor row in numrange:\n    for col in numrange:\n        #alternate between -1 and 1\n        mat[row,col] = (-1)**(row+col)\ndisp(mat)",
      "execution_count": 18,
      "outputs": [
        {
          "data": {
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}1.0 & -1.0 & 1.0 & -1.0 & 1.0 & -1.0\\\\-1.0 & 1.0 & -1.0 & 1.0 & -1.0 & 1.0\\\\1.0 & -1.0 & 1.0 & -1.0 & 1.0 & -1.0\\\\-1.0 & 1.0 & -1.0 & 1.0 & -1.0 & 1.0\\end{matrix}\\right]$",
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      "cell_type": "code",
      "source": "x,y = sym.symbols('x y')\nexp = (4+x)*(2-y)\nnumrange = range(0,3)\nmat = np.zeros([3,3])\nfor i in numrange:\n    for j in numrange:\n        mat[i,j] = exp.subs({x:i,y:j})\n\ndisp(mat)",
      "execution_count": 24,
      "outputs": [
        {
          "data": {
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}8.0 & 4.0 & 0.0\\\\10.0 & 5.0 & 0.0\\\\12.0 & 6.0 & 0.0\\end{matrix}\\right]$",
            "text/plain": "<IPython.core.display.Math object>"
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      "cell_type": "code",
      "source": "def multiplicationMatrix(numRange = range(1,11)):\n    end = len(numRange)\n    mat = np.zeros([end,end],dtype=int)\n    for row in numRange:\n        for col in numRange:\n            mat[row-1,col-1] = row * col\n    disp(mat)\nmultiplicationMatrix()",
      "execution_count": 44,
      "outputs": [
        {
          "data": {
            "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10\\\\2 & 4 & 6 & 8 & 10 & 12 & 14 & 16 & 18 & 20\\\\3 & 6 & 9 & 12 & 15 & 18 & 21 & 24 & 27 & 30\\\\4 & 8 & 12 & 16 & 20 & 24 & 28 & 32 & 36 & 40\\\\5 & 10 & 15 & 20 & 25 & 30 & 35 & 40 & 45 & 50\\\\6 & 12 & 18 & 24 & 30 & 36 & 42 & 48 & 54 & 60\\\\7 & 14 & 21 & 28 & 35 & 42 & 49 & 56 & 63 & 70\\\\8 & 16 & 24 & 32 & 40 & 48 & 56 & 64 & 72 & 80\\\\9 & 18 & 27 & 36 & 45 & 54 & 63 & 72 & 81 & 90\\\\10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 & 90 & 100\\end{matrix}\\right]$",
            "text/plain": "<IPython.core.display.Math object>"
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