[Solved] MATH307 Group Homework8

Instructions: Read textbook pages 149 to 155 before working on the homework problems. Show all steps to get full credits.

3 0 1

1. Let A = 0 2 1 , determine whether A is nondefective, i.e., whether

0 0 2

the algebra multiplicity and the geometric multiplicity are identical for all eigenvalues.

2. Let A be a Hermitian matrix, prove that eigenvectors corresponding to distinct eigenvalues of A are orthogonal. Note this is stronger than eigenvectors of distinct eigenvalues of a general matrix are linearly independent.
3. Let A = UV be a singular value decomposition of A, prove that V ()V is an eigendecomposition of AA.

2 2

4. Use SVD to solve Ax = b. Let A = UV T with

2 0 0 1 ,V ,b .