Arbitrary positive powers of semicirculant and r-circulant matrices

TL;DR

This paper introduces a new recursive approach for efficiently computing the entries of arbitrary positive powers of semicirculant and r-circulant matrices, expanding computational tools in matrix analysis.

Contribution

It presents the first recursive method that does not rely on assumptions to compute matrix powers for semicirculant and r-circulant matrices.

Findings

Recursive formulas for matrix powers derived

Method applicable without assumptions

Enhanced computational efficiency for matrix powers

Abstract

We provide a novel recursive method, which does not require any assumption, to compute the entries of the kth power of a semicirculant matrix. As an application, a method for computing the entries of the kth power of r-circulant matrices is also presented.