Trace of a matrix equals sum of its determinants?

[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.

 

[Hurkyl]

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

 

[samspotting]

Ah I see, the trace is similarity invariant. thanks