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

Abstract EN

We prove that any k-circulant matrix and any even order skew k-circulant matrix are diagonalizable for any k∈ℂ.

Then, we propose two algorithms for computing the square roots of the k-circulant matrix and the skew k-circulant matrix, respectively.

In particular, we show that the square roots of the k-circulant matrix are still k-circulant matrices.

Both the theoretical analysis and the numerical experiments show that our algorithms are faster than the standard Schur method.