1. Explain what happens when the inverse power method is applied to the matrix 2. Prove that the left eigenvectors of a symmetric matrix are eigenvectors. Let and be two distinct eigenvalues of ...

1.

Explain what happens when the inverse power method is applied to the matrix

2.

Prove that the left eigenvectors of a symmetric matrix are eigenvectors.

Let

and

be two distinct eigenvalues of

Show that all left eigenvectors associated with

are orthogonal to all right eigenvectors associated with

3.

shift strategy will enable more rapid computation of the eigenvalues? Explain.