Instructions: Read textbook pages 89 to 94 before working on the homework problems. Show all steps to get full credits.
- 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.
- If all singular values of A∈Fm×n with m>n are positive, is A∗A invertible?
How about AA∗? Use SVD to justify your answers.
