Trace of a matrix equals sum of its determinants?

1. Feb 8, 2009

samspotting

If a matrix is diagonalizable, how does its trace equal the sum of its eigenvalues?

I can't find a proof for this anywhere.

2. Feb 8, 2009

Hurkyl

Staff Emeritus
What is the trace of a diagonal matrix? What are the algebraic properties of trace?

3. Feb 9, 2009

samspotting

Ah I see, the trace is similarity invariant. thanks