Å−2
1. Compute eigenvalues and eigenvectors of matrix
−1
−2ã
.
−3
2. Suppose λ is an eigenvalue of an invertible matrix A corresponding to an eigenvector v, provide a set of eigenvalue and eigenvector for (A−1)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 m×n matrix, prove that the eigenvalues of A∗A are real valued and non-negative.
