[SOLVED] MATH307-Individual Homework 17

Description

1. If A=UΣV^∗ is a singular value decomposition of a square matrix A, then A is invertible if and only if all diagonal entries of Σ are nonzero. Assuming that A is invertible, write A⁻¹ in terms of factors of the singular value decomposition of A.
2. If all singular values of A∈F^m×n with m>n are positive, is A^∗A invertible?

How about AA^∗? Use SVD to justify your answers.