A is a matrix of order n. It is proved that tr (a ^ k) = the sum of the k-th power of the eigenvalues of A

A is a matrix of order n. It is proved that tr (a ^ k) = the sum of the k-th power of the eigenvalues of A

Let A1,..., an be the eigenvalue of A
Then A1 ^ k,..., an ^ k is the eigenvalue of a ^ k (theorem conclusion)
So tr (a ^ k) = A1 ^ k +... + an ^ K. (theorem)