39 Welcome to the spoken tutorial on Matrices. |
40 Welcome to the spoken tutorial on Matrices. |
40 |
41 |
41 {{{ switch to next slide, outline slide }}} |
42 {{{ switch to next slide, outline slide }}} |
42 |
43 |
43 In this tutorial we will learn about matrices, creating matrices using |
44 In this tutorial we will learn about matrices, creating matrices using |
44 direct data, by converting a list, matrix operations. Finding inverse |
45 direct data, by converting a list and matrix operations. Finding |
45 of a matrix, determinant of a matrix, eigen values and eigen vectors |
46 inverse of a matrix, determinant of a matrix, eigen values and eigen |
46 of a matrix, norm and singular value decomposition of matrices. |
47 vectors of a matrix, norm and singular value decomposition of |
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48 matrices. |
47 |
49 |
48 {{{ creating a matrix }}} |
50 {{{ creating a matrix }}} |
49 |
51 |
50 All matrix operations are done using arrays. Thus all the operations |
52 All matrix operations are done using arrays. Thus all the operations |
51 on arrays are valid on matrices also. A matrix may be created as, |
53 on arrays are valid on matrices also. A matrix may be created as, |
156 |
158 |
157 Matrix name dot capital T will give the transpose of a matrix |
159 Matrix name dot capital T will give the transpose of a matrix |
158 |
160 |
159 {{{ switch to next slide, Frobenius norm of inverse of matrix }}} |
161 {{{ switch to next slide, Frobenius norm of inverse of matrix }}} |
160 |
162 |
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163 .. #[punch: arange has not been introduced.] |
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164 |
161 Now let us try to find out the Frobenius norm of inverse of a 4 by 4 |
165 Now let us try to find out the Frobenius norm of inverse of a 4 by 4 |
162 matrix, the matrix being, |
166 matrix, the matrix being, |
163 :: |
167 :: |
164 |
168 |
165 m5 = arange(1,17).reshape(4,4) |
169 m5 = arange(1,17).reshape(4,4) |
175 And here is the solution, first let us find the inverse of matrix m5. |
179 And here is the solution, first let us find the inverse of matrix m5. |
176 :: |
180 :: |
177 |
181 |
178 im5 = inv(m5) |
182 im5 = inv(m5) |
179 |
183 |
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184 .. #[punch: we don't need to show this way of calculating the norm, do |
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185 .. we? even if we do, we should show it in the "array style". |
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186 .. something like: |
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187 .. sqrt(sum(each * each))] |
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188 |
180 And the Frobenius norm of the matrix ``im5`` can be found out as, |
189 And the Frobenius norm of the matrix ``im5`` can be found out as, |
181 :: |
190 :: |
182 |
191 |
183 sum = 0 |
192 sum = 0 |
184 for each in im5.flatten(): |
193 for each in im5.flatten(): |
185 sum += each * each |
194 sum += each * each |
186 print sqrt(sum) |
195 print sqrt(sum) |
187 |
196 |
188 {{{ switch to next slide, infinity norm }}} |
197 {{{ switch to next slide, infinity norm }}} |
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198 .. #[punch: similarly for this section.] |
189 |
199 |
190 Now try to find out the infinity norm of the matrix im5. The infinity |
200 Now try to find out the infinity norm of the matrix im5. The infinity |
191 norm of a matrix is defined as the maximum value of sum of the |
201 norm of a matrix is defined as the maximum value of sum of the |
192 absolute of elements in each row. Pause here and try to solve the |
202 absolute of elements in each row. Pause here and try to solve the |
193 problem yourself. |
203 problem yourself. |
194 |
204 |
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205 |
195 The solution for the problem is, |
206 The solution for the problem is, |
196 :: |
207 :: |
197 |
208 |
198 sum_rows = [] |
209 sum_rows = [] |
199 for i in im5: |
210 for i in im5: |
239 Let us find out the eigen values and eigen vectors of the matrix |
250 Let us find out the eigen values and eigen vectors of the matrix |
240 m5. We can do it as, |
251 m5. We can do it as, |
241 :: |
252 :: |
242 |
253 |
243 eig(m5) |
254 eig(m5) |
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255 |
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256 |
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257 .. #[punch: has the tuple word been introduced?] |
244 |
258 |
245 Note that it returned a tuple of two matrices. The first element in |
259 Note that it returned a tuple of two matrices. The first element in |
246 the tuple are the eigen values and the second element in the tuple are |
260 the tuple are the eigen values and the second element in the tuple are |
247 the eigen vectors. Thus the eigen values are, |
261 the eigen vectors. Thus the eigen values are, |
248 :: |
262 :: |