A Family of Determinants Associated with a Square Matrix

We associate with a matrix over an arbitrary field an infinite family of matrices whose sizes vary from one to infinity; their entries are traces of powers of the original matrix. We explicitly evaluate the determinants of matrices in our family. The work is motivated by applications to graph spectra. 1. A two-parameter family of matrices Let K be a field, and let G be a square matrix of arbitrary finite size, with entries in K. We will denote by tr A the trace of a square matrix. Let t ≥ 1 and l ≥ 0 be any integers. Set