{
 "metadata": {
  "language": "Julia",
  "name": "symmetric matrices and vector spaces"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": "A matrix is symmetric if A=A'"
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "Diagonal matrices are symmetric"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "D=diagm(1:5);\n(D,D')",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": "(\n5x5 Array{Int64,2}:\n 1  0  0  0  0\n 0  2  0  0  0\n 0  0  3  0  0\n 0  0  0  4  0\n 0  0  0  0  5,\n\n5x5 Array{Int64,2}:\n 1  0  0  0  0\n 0  2  0  0  0\n 0  0  3  0  0\n 0  0  0  4  0\n 0  0  0  0  5)"
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "issym(D)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": "true"
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "If S is symmetric, inv(S) ' = inv(S') = inv(S) hence inv(S) is symmetric"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "S=[3 12;12 5]",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": "2x2 Array{Int64,2}:\n  3  12\n 12   5"
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "round(inv(S),7)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": "2x2 Array{Float64,2}:\n -0.0387597   0.0930233\n  0.0930233  -0.0232558"
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "If R is any rectangular matrix R'*R  is symmetric: Why?"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "R=rand(5,2); round(R*R',3)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": "5x5 Array{Float64,2}:\n 0.871  1.166  0.816  0.085  0.987\n 1.166  1.598  1.004  0.113  1.35 \n 0.816  1.004  0.972  0.081  0.856\n 0.085  0.113  0.081  0.008  0.096\n 0.987  1.35   0.856  0.096  1.14 "
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "issym(R*R')",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": "true"
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "a=R'*R",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": "2x2 Array{Float64,2}:\n 1.7064   1.93981\n 1.93981  2.88402"
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "Fact without proof: if S is symmetric, elimination produces S=LDL'",
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": "Permutation Matrices"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "A=randn(5,5);\n(L,U,P)=lu(A);\n(round(L,3),round(U,3),round(P,1))",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": "(\n5x5 Array{Float64,2}:\n  1.0     0.0     0.0     0.0    0.0\n  0.835   1.0     0.0     0.0    0.0\n  0.607   0.411   1.0     0.0    0.0\n -0.885   0.216  -0.248   1.0    0.0\n -0.519  -0.577  -0.639  -0.984  1.0,\n\n5x5 Array{Float64,2}:\n -0.831  -1.29    0.041   0.83    2.648\n  0.0     2.539   1.151  -0.157  -4.152\n  0.0     0.0    -1.898  -1.537   0.432\n  0.0     0.0     0.0     0.841   4.13 \n  0.0     0.0     0.0     0.0     1.541,\n\n5x5 Array{Float64,2}:\n 0.0  1.0  0.0  0.0  0.0\n 0.0  0.0  1.0  0.0  0.0\n 0.0  0.0  0.0  0.0  1.0\n 1.0  0.0  0.0  0.0  0.0\n 0.0  0.0  0.0  1.0  0.0)"
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "(round(P*A,3),round(L*U,3))",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": "(\n5x5 Array{Float64,2}:\n -0.831  -1.29    0.041   0.83    2.648\n -0.694   1.461   1.186   0.537  -1.941\n -0.505   0.261  -1.4    -1.097   0.332\n  0.736   1.689   0.682   0.453   0.784\n  0.431  -0.794   0.527  -0.186  -1.78 ,\n\n5x5 Array{Float64,2}:\n -0.831  -1.29    0.041   0.83    2.648\n -0.694   1.461   1.186   0.537  -1.941\n -0.505   0.261  -1.4    -1.097   0.332\n  0.736   1.689   0.682   0.453   0.784\n  0.431  -0.794   0.527  -0.186  -1.78 )"
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": "Vector Spaces"
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": "A real vector space is a set of \"vectors\" with an addition and multiplication by scalars that satisfies eight rules (rules coming soon)"
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "vectors in standard format"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "v=rand(0:9, 5);  w=rand(0:9,5); [v w]",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": "5x2 Array{Int64,2}:\n 4  0\n 6  3\n 8  9\n 3  8\n 8  3"
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "v*10",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": "5-element Array{Int64,1}:\n 40\n 60\n 80\n 30\n 80"
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "v+w",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": "5-element Array{Int64,1}:\n  4\n  9\n 17\n 11\n 11"
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "arrays themselves are vectors"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "A=rand(0:9,2,2); B=rand(0:9,2,2); (A,B)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 31,
       "text": "(\n2x2 Array{Int64,2}:\n 3  3\n 9  5,\n\n2x2 Array{Int64,2}:\n 2  9\n 7  7)"
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "A*10",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 32,
       "text": "2x2 Array{Int64,2}:\n 30  30\n 90  50"
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "A+B",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 33,
       "text": "2x2 Array{Int64,2}:\n  5  12\n 16  12"
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "functions are vectors"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "typeof(sin)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": "Function"
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "sin+cos",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "LoadError",
       "evalue": "no method +(Function,Function)\nat In[36]:1",
       "output_type": "pyerr",
       "traceback": [
        "no method +(Function,Function)\nat In[36]:1"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "+(f::Function,g::Function)=x->f(x)+g(x);",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "(sin+cos)(12)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 38,
       "text": "0.3072810407320572"
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "sin(12)+cos(12)\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 39,
       "text": "0.3072810407320572"
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "*(c::Number,f::Function) = x->c*f(x);",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "(10*sin)(5)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 40,
       "text": "-9.589242746631385"
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "10*sin(5)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 41,
       "text": "-9.589242746631385"
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "x=-10:.001:10; plot(x, (sin+cos)(x));",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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    {
     "cell_type": "code",
     "collapsed": false,
     "input": "plot( x, (10cos)(x));",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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     "metadata": {},
     "source": "1. x+y = y+x                                             COMMUTATIVE LAW OF ADDITION\n2. x+ (y+z) = (x+y)+z                                    ASSOCIATIVE LAW OF ADDITION\n3. There is a unique \"zero vector\" such that x+0 = x     ADDITIVE IDENTIY\n4. For each x there is a -x such that x + (-x) = 0       ADDITIVE INVERSES\n5. 1 * x = x                                             MULTIPLICATIVE IDENTITY\n6. (c1*c2)x=c1*(c2*x)                                    ASSOCIATIVE LAW OF SCALAR,SCALAR,VECTOR MULTIPLICATIONS\n7. c(x+y)-cx+cy                                          MULTIPLICATION DISTRIBUTES OVER VECTOR ADDITION\n8. (c1+c2)x = c1 x + c2 x                                SCALAR ADDITION DISTRIBUTES OVER MULTIPLICATION"
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    {
     "cell_type": "code",
     "collapsed": false,
     "input": "Subspaces: Are sums in the space?  Are constant times vector in the space?",
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}