On the trace of powers of square matrices

Year 2021, Volume: 50 Issue: 1, 14 - 23, 04.02.2021

Kailash Patil

https://doi.org/10.15672/hujms.558995

Abstract

Using Cayley-Hamilton equation for matrices, we obtain a simple formula for trace of powers of a square matrix. The formula becomes simpler in particular cases. As a consequence, we also demonstrate the formula for trace of negative powers of a matrix.

Keywords

trace of a matrix, powers of a matrix, Cayley-Hamilton theorem, spectral radius

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