A closed-form expression for the kth power of semicirculant and r-circulant matrices

TL;DR

This paper derives explicit formulas for computing the kth power of semicirculant and r-circulant matrices using determinant-based methods, simplifying calculations in matrix analysis.

Contribution

It introduces a novel closed-form expression for the powers of semicirculant and r-circulant matrices, expanding analytical tools in matrix theory.

Findings

Closed-form expression for semicirculant matrix powers

Closed-form expression for r-circulant matrix powers

Simplifies computation of matrix powers

Abstract

We derive a closed-form expression for the kth power of semicirculant matrices by using the determinant of certain matrices. As an application, a closed-form expression for the kth power of r-circulant matrices is also povided.