1. Using the Bauer-Fike theorem, show that if is normal, and is an eigenvalue of then What does this say about the conditioning of the eigenvalues 2. Show that Equation 18.37 is correct. 3. Show...

1. Using the Bauer-Fike theorem, show that if

is normal, and

is an eigenvalue of

then

What does this say about the conditioning of the eigenvalues

2. Show that Equation 18.37 is correct.

3. Show that Equation 18.39 is correct.

4. What are the condition numbers for the eigenvalues of a symmetric matrix?

5. Using the matrix of Example 18.13, show that the Schur’s triangularization is not unique.

normalized eigenvector v1 such that