Trace of the matrix power Say I have matrix $A = \begin{bmatrix}
a & 0 & -c\\
0 & b & 0\\
-c & 0 & a 
\end{bmatrix}$.
What is matrix trace
tr(A^200)
Thanks much! 

You may do it by first computing matrix powers and then you may calculate whatever you want. Now question is how to calculate matrix power for a given matrix, say $A$? Your goal here is to develop a useful factorization $A = PDP^{-1}$, when $A$ is $n\times n$ matrix.The matrix $D$ is a diagonal matrix (i.e. entries off the main diagonal are all zeros).
Then $A^k =PD^kP^{-1} $. $D^k$ is trivial to compute. Note that columns of $P$ are n linearly
independent eigenvectors of $A$.
