[Solved] MATH307 Individual Homework17

Instructions: Read textbook pages 89 to 94 before working on the homework problems. Show all steps to get full credits.

1. If A=UV is a singular value decomposition of a square matrix A, then A is invertible if and only if all diagonal entries of are nonzero. Assuming that A is invertible, write A¹ in terms of factors of the singular value decomposition of A.
2. If all singular values of AF^mn with m>n are positive, is AA invertible?

How about AA? Use SVD to justify your answers.