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21 Welcome to the spoken tutorial on Matrices. |
21 Welcome to the spoken tutorial on Matrices. |
22 |
22 |
23 {{{ switch to next slide, outline slide }}} |
23 {{{ switch to next slide, outline slide }}} |
24 |
24 |
25 In this tutorial we will learn about matrices, creating matrices and |
25 In this tutorial we will learn about matrices, creating matrices using |
26 matrix operations. |
26 direct data, by converting a list, matrix operations. Finding inverse |
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27 of a matrix, determinant of a matrix, eigen values and eigen vectors |
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28 of a matrix, norm and singular value decomposition of matrices. |
27 |
29 |
28 {{{ creating a matrix }}} |
30 {{{ creating a matrix }}} |
29 |
31 |
30 All matrix operations are done using arrays. Thus all the operations |
32 All matrix operations are done using arrays. Thus all the operations |
31 on arrays are valid on matrices also. A matrix may be created as, |
33 on arrays are valid on matrices also. A matrix may be created as, |
86 function ``multiply()`` |
88 function ``multiply()`` |
87 :: |
89 :: |
88 |
90 |
89 multiply(m3,m2) |
91 multiply(m3,m2) |
90 |
92 |
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93 {{{ switch to next slide, Matrix multiplication (cont'd) }}} |
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94 |
91 Now let us see an example for matrix multiplication. For doing matrix |
95 Now let us see an example for matrix multiplication. For doing matrix |
92 multiplication we need to have two matrices of the order n by m and m |
96 multiplication we need to have two matrices of the order n by m and m |
93 by r and the resulting matrix will be of the order n by r. Thus let us |
97 by r and the resulting matrix will be of the order n by r. Thus let us |
94 first create two matrices which are compatible for multiplication. |
98 first create two matrices which are compatible for multiplication. |
95 :: |
99 :: |
106 thus unlike in array object ``star`` can be used for matrix multiplication |
110 thus unlike in array object ``star`` can be used for matrix multiplication |
107 in matrix object. |
111 in matrix object. |
108 |
112 |
109 {{{ switch to next slide, recall from arrays }}} |
113 {{{ switch to next slide, recall from arrays }}} |
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114 |
111 As we already saw in arrays, the functions ``identity()``, |
115 As we already saw in arrays, the functions ``identity()`` which |
112 ``zeros()``, ``zeros_like()``, ``ones()``, ``ones_like()`` may also be |
116 creates an identity matrix of the order n by n, ``zeros()`` which |
113 used with matrices. |
117 creates a matrix of the order m by n with all zeros, ``zeros_like()`` |
114 |
118 which creates a matrix with zeros with the shape of the matrix passed, |
115 {{{ switch to next slide, matrix operations }}} |
119 ``ones()`` which creates a matrix of order m by n with all ones, |
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120 ``ones_like()`` which creates a matrix with ones with the shape of the |
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121 matrix passed. These functions can also be used with matrices. |
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122 |
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123 {{{ switch to next slide, more matrix operations }}} |
116 |
124 |
117 To find out the transpose of a matrix we can do, |
125 To find out the transpose of a matrix we can do, |
118 :: |
126 :: |
119 |
127 |
120 print m4 |
128 print m4 |
176 we do, |
184 we do, |
177 :: |
185 :: |
178 |
186 |
179 norm(im5) |
187 norm(im5) |
180 |
188 |
181 Euclidean norm is also called Frobenius norm. |
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182 |
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183 And to find out the Infinity norm of the matrix im5, we do, |
189 And to find out the Infinity norm of the matrix im5, we do, |
184 :: |
190 :: |
185 |
191 |
186 norm(im5,ord=inf) |
192 norm(im5,ord=inf) |
187 |
193 |