Complex eigenvalues modal analysis

Are complex eigenvalues diagonalizable?

If a matrix has distinct complex eigenvalues, then it is also diagonalizable, but it similar to a diagonal matrix with complex entries.
The geometric interpretation of such a matrix is a subtle question, which is treated in detail in the full version of the book..

How do you know if a matrix has complex eigenvalues?

For a 2x2 matrix for example, we can see that if (Trace)2−4u221.

1. Determinant\x26lt;0 , the matrix has complex eigenvalues