A formula for the trace of symmetric powers of matrices
  We present a formula for the trace of any symmetric power of a $n\times n$ matrix (with coefficients in a field) in terms of the ordinary powers of the matrix, an arbitrarily chosen linear function which vanishes on the identity matrix, and $n-2$ polynomial functions defined recursively. 
Jose Luis Cisneros, Rafael Herrera, Noemi Santana
math.DG