[Solved] MATH307 Individual Homework16

Instructions: Read textbook pages 147 to 148 before working on the homework problems. Show all steps to get full credits.

2. Suppose is an eigenvalue of an invertible matrix A corresponding to an eigenvector v, provide a set of eigenvalue and eigenvector for (A¹)³. Note you may use the fact that the eigenvalues of an invertible matrix are nonzero.
3. A matrix P is called a projector if P² = P. Prove the eigenvalues of a projector are either 0 or 1.
4. Let A be a mn matrix, prove that the eigenvalues of AA are real valued and non-negative.