Let A be a nonsingular 2 2 matrix with singular value decomposition A = USVT and
Chapter 6, Problem 20(choose chapter or problem)
Let A be a nonsingular 2 2 matrix with singular value decomposition A = USVT and singular values s1 = s11 and s2 = s22. Explain why each of the following are true: (a) AV = US (b) Av1 = s1u1 and Av2 = s2u2. (c) v1 and v2 are orthogonal unit vectors and the images Av1 and Av2 are also orthogonal. (d) _Av1_ = s1 and _Av2_ = s2. 2
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