matrices.org
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7:9794cc414498 8:e5194abc864f
       
     1 * Matrices
       
     2 *** Outline
       
     3 ***** Introduction
       
     4 ******* Why do we want to do that?
       
     5 ******* We shall use arrays (introduced before) for matrices
       
     6 ******* Arsenal Required
       
     7 ********* working knowledge of arrays
       
     8 ***** Various matrix operations
       
     9 ******* Transpose
       
    10 ******* Sum of all elements
       
    11 ******* Element wise operations
       
    12 ******* Matrix multiplication
       
    13 ******* Inverse of a matrix
       
    14 ******* Determinant
       
    15 ******* eigen values/vectors
       
    16 ******* svd
       
    17 ***** Other things available?
       
    18 *** Script
       
    19     Welcome. 
       
    20     
       
    21     In this tutorial, you will learn how to perform some common matrix
       
    22     operations. We shall look at some of the functions available in
       
    23     pylab. Note that, this tutorial just scratches the surface and
       
    24     there is a lot more that can be done. 
       
    25 
       
    26     Let's begin with finding the transpose of a matrix. 
       
    27     
       
    28     In []: a = array([[ 1,  1,  2, -1],
       
    29     ...:            [ 2,  5, -1, -9],
       
    30     ...:            [ 2,  1, -1,  3],
       
    31     ...:            [ 1, -3,  2,  7]])
       
    32 
       
    33     In []: a.T
       
    34 
       
    35     Type a, to observe the change in a. 
       
    36     In []: a
       
    37     
       
    38     Now we shall look at adding another matrix b, to a. It doesn't
       
    39     require anything special, just use the + operator. 
       
    40     
       
    41     In []: b = array([[3, 2, -1, 5],
       
    42                       [2, -2, 4, 9],
       
    43                       [-1, 0.5, -1, -7],
       
    44                       [9, -5, 7, 3]])
       
    45     In []: a + b
       
    46 
       
    47     What do you expect would be the result, if we used * instead of
       
    48     the + operator? 
       
    49 
       
    50     In []: a*b
       
    51     
       
    52     You get an element-wise product of the two arrays and not a matrix
       
    53     product. To get a matrix product, we use the dot function. 
       
    54     
       
    55     In []: dot(a, b)
       
    56 
       
    57     The sum function returns the sum of all the elements of the
       
    58     array. 
       
    59     
       
    60     In []: sum(a)
       
    61 
       
    62     The inv command returns the inverse of the matrix. 
       
    63     In []: inv(a)
       
    64 
       
    65     In []: det(a)
       
    66 
       
    67     In []: eig(a)
       
    68     Returns the eigenvalues and the eigen vectors. 
       
    69     
       
    70     In []: eigvals(a)
       
    71     Returns only the eigenvalues. 
       
    72 
       
    73     In []: svd(a)
       
    74     Singular Value Decomposition 
       
    75 
       
    76 *** Notes
       
    77