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.
