gibson:teaching:fall-2014:iam961:iam-961-hw2
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gibson:teaching:fall-2014:iam961:iam-961-hw2 [2014/09/25 13:14] gibson created |
gibson:teaching:fall-2014:iam961:iam-961-hw2 [2014/09/25 13:37] (current) gibson |
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| Case 2: Repeated singular values | Case 2: Repeated singular values | ||
| - | - Create a random 4 x 4 complex matrix $A$ with $\sigma_1 = \sigma_2 > \sigma_3 > sigma_4$ and known SVD $U_1 \Sigma_1 V_1^*$ | + | - Create a random 4 x 4 complex matrix $A$ with $\sigma_1 = \sigma_2 > \sigma_3 > \sigma_4$ and known SVD $U_1 \Sigma_1 V_1^*$ |
| - Compute the SVD $U_2 \Sigma_2 V_2^*$ of $A$. | - Compute the SVD $U_2 \Sigma_2 V_2^*$ of $A$. | ||
| - Of the two SVDs, what should be the same? What is likely to be different? | - Of the two SVDs, what should be the same? What is likely to be different? | ||
| - Show that the first two columns of $U_1$ span the same 2d subspace as the first two columns of $U_2$ (do this by showing that the first two columns of $U_1$ are in the span of the first two columns of $U_2$, and vice versa). | - Show that the first two columns of $U_1$ span the same 2d subspace as the first two columns of $U_2$ (do this by showing that the first two columns of $U_1$ are in the span of the first two columns of $U_2$, and vice versa). | ||
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| + | Keep a diary of your work in Matlab (''diary on''). Edit the diary text file to remove mistakes and extraneous material, and turn in a printout of the text file. Use comments to explain what you are doing, in the style of the [[gibson:teaching:fall-2014:iam961:svddemo | SVD demo ]] | ||
gibson/teaching/fall-2014/iam961/iam-961-hw2.1411676079.txt.gz ยท Last modified: 2014/09/25 13:14 by gibson
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