U= -0.86 -0.11 -0.5 0.31 0.68 -0.67 0.41 -0.73 -0.55 12.48 0 0 0 06.34 0 0 0 0 0 0 V = 0.66 -0.03 -0.35 0.66 -0.13 -0.9

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U 0 86 0 11 0 5 0 31 0 68 0 67 0 41 0 73 0 55 12 48 0 0 0 06 34 0 0 0 0 0 0 V 0 66 0 03 0 35 0 66 0 13 0 9 1 (104.28 KiB) Viewed 28 times

U= -0.86 -0.11 -0.5 0.31 0.68 -0.67 0.41 -0.73 -0.55 12.48 0 0 0 06.34 0 0 0 0 0 0 V = 0.66 -0.03 -0.35 0.66 -0.13 -0.9 -0.39 -0.13 0.65 0.08 -0.16 -0.73 -0.34 0.42 -0.84 -0.08 (a) (1 point) What is the size of the original matrix A? Explain your reasoning. (b) (1 point) What is UUT? Do not compute this by hand! Explain how you know what UUT is without any computation. Be sure to specify the matrix size if you just describe it in words. (c) (1 point) What is VVT? Do not compute this by hand! Explain how you know what VVT is without any computation. Be sure to specify the matrix size if you just describe it in words. (d) (1 point) Use the SVD to determine the rank of A. Explain your reasoning. (e) (2 points) What are the eigenvalues of AAT? What are the eigenvalues of AT A? Include multi- plicity, but be careful about the sizes of each matrix! () (2 points) Consider the first term in the singular value decomposition in vector form: -0.86 0u1V1 = 12.48 0.31 [0.66 -0.13 0.65 -0.34] Explain why this is a reasonable approxi- 0.41 mation to the matrix A. How many more terms like this would you need to add to get A exactly? T