A Note on the Square Roots of a Class of Circulant Matrices

Abstract

We prove that anyk-circulant matrix and any even order skewk-circulant matrix are diagonalizable for anyk∈ℂ. Then, we propose two algorithms for computing the square roots of thek-circulant matrix and the skewk-circulant matrix, respectively. In particular, we show that the square roots of thek-circulant matrix are stillk-circulant matrices. Both the theoretical analysis and the numerical experiments show that our algorithms are faster than the standard Schur method.