This question is about Eigenvalues and Eigenvectors For S1 p

This question is about Eigenvalues and Eigenvectors.

For S1: please give an example. Thank you so much.

In S3, it is the Complex Euclidean Inner Product.

Solution

Answer for S1 is false because 5x5 matrix contains 5 roots for eigen values . We know that, complex roots appears in pairs. So, atmost 2 pairs of complex roots ( 4 values ) will be eigen values and remaining root is real. Any 5x5 matrix is an example

0 1 0 0 0

-1 1 0 0 0

0 1 2 0 0

1 2 3 0 1

0 0 0 -1 1

0