1. Using matrix of verify that the eigenvalues of T and are equal. Can you say the same about the eigenvectors If and are upper-triangular matrices, are the eigenvalues of the sum of the...

1. Using matrix of

verify that the eigenvalues of

^T
and

are equal. Can you say the same about the eigenvectors

If

and

are

upper-triangular matrices, are the eigenvalues of

the sum of the eigenvalues and

and

Is part

true for two arbitrary
matrices

and

2. If A is an

nonsingular matrix, prove that

<sup>−1

T

T

−1</sup>