What is the trace of AnA^nAn if the eigenvalues of AAA are λ1,λ2,…,λk\lambda_1, \lambda_2, \dots, \lambda_kλ1,λ2,…,λk?
∑i=1kλin\sum_{i=1}^k \lambda_i^n∑i=1kλin
(∑λi)n(\sum \lambda_i)^n(∑λi)n
∏λin\prod \lambda_i^n∏λin
n∑λin \sum \lambda_in∑λi