Description
1. Compute eigenvalues and eigenvectors of matrix Å
−2 −2
−1 −3
ã
.
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 P
2 = 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.
