Question

True or False?

1. If σ is a singular value of a matrix A, then σ is an eigenvalue of ATA Answer: 2. Every matrix has the same singular values as its transpose Answer: 3. A matrix has a pseudo-inverse if and only if it is not invertible. Answer: 4. If matrix A has rank k, then A has k singular values Answer:_ 5. Every matrix has a singular value decomposit ion Answer:_ 6. Every matrix has a unique singular value decomposition Answer- 7. In a singular value decomposition Uy/T of A, each diagonal entry of Σ is a singular value of A Answer:_ 8. If UEVT is a singular value decomposition of A, then ΥΣυΤΕ a singular value decomposition of AT. Answer: 9. If υΣνι, is a singular value decomposition of A having rank k, and if W ColA, then the , k and orthogonal projection matrix for W is given by Po-UDUT, where dií = 1 if i = 1, 2, dij -0 otherwise Answer:- 10. If A is an m × n matrix and UΣⅤr, is a singular value decomposition of A, then a vector u in Rn that minimizes IAu-bil is VDtUTb where Σt is the same as matrix Σ with singular values Ơk replaced with 1/ơk. Answer: 11. If A is an m x n matrix and UEVT is a singular value decomposition of A, then VUb is the unique vector u in R" that minimizes ||Au b Answer:

Answer 1

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