TITLE: Trace, determinant and eigenvalues for non-diagonalizable matrix
QUESTION [5 upvotes]: Is the trace and determinant equal to the sum and product, respectively, of the eigenvalues even if a matrix is not diagonalizable? 
The proof I've seen for the trace equaling the sum of the eigenvalues and the determinant equaling the eigenvalues assumes a matrix can be written as $PDP^{-1}$. But if it is not diagonalizable, then we can't possibly write $PDP^{-1}$. So what happens then?

REPLY [2 votes]: Yes. If the matrix is not diagonalizable then still it can be written in Jordan canonical form. And trace relation and determinant relation can be determined using this.