A formula for the trace of symmetric powers of matrices

2014/11/03 by José Luis Cisneros, Jose Luis Cisneros, Cisneros, Jose Luis +5
Computer Science · Mathematics · #15A69 #15A72 #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #math.DG #msc:15A69 #msc:15A72

paper · pdf · doi:10.48550/arxiv.1411.0524

arxiv created 2014/11/03 · openalex publication_date 2014/11/03 · arxiv updated 2014/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a formula for the trace of any symmetric power of a n× 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.

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