Question: Let A be a nonsingular 2 2 matrix with singular value decomposition A = USVT and singular values s1 = s11, .s2 = s22.

Let A be a nonsingular 2 × 2 matrix with singular value decomposition A = USVT and singular values s1 = s11, .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.
Set
A = [1, 1; 0.5, -0.5]
and use MATLAB to verify each of the above statements.

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a If A USV T then AV USV T V US b AV Av 1 Av 2 and US s 1 u 1 s 2 u 2 Since AV US their c... View full answer

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