{
 "metadata": {
  "name": "",
  "signature": "sha256:72ca7769e63a40b2f7f89ae8f816dcd0df3658bb19519d8c95b2f6a5e99413ec"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy import Symbol, Matrix\n",
      "from sympy.interactive import printing\n",
      "printing.init_printing()\n",
      "\n",
      "dt = Symbol('\\Delta t')\n",
      "\n",
      "Q = Matrix([[.5*dt**2], [.5*dt**2], [dt], [dt]])\n",
      "Q*Q.T\n",
      "\n",
      "\n",
      "Q = Matrix([[.5*dt**2], [dt]])\n",
      "Q*Q.T"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{matrix}0.25 \\Delta t^{4} & 0.5 \\Delta t^{3}\\\\0.5 \\Delta t^{3} & \\Delta t^{2}\\end{matrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAKQAAAAzBAMAAADr+L6JAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nD+iXYj8NWuVEAAAAAElFTkSuQmCC\n",
       "prompt_number": 8,
       "text": [
        "\u23a1             4              3\u23a4\n",
        "\u23a20.25\u22c5\\Delta t   0.5\u22c5\\Delta t \u23a5\n",
        "\u23a2                             \u23a5\n",
        "\u23a2            3             2  \u23a5\n",
        "\u23a30.5\u22c5\\Delta t      \\Delta t   \u23a6"
       ]
      }
     ],
     "prompt_number": 8
    }
   ],
   "metadata": {}
  }
 ]
}