We prove that any -circulant matrix and any even order skew -circulant matrix are diagonalizable for any . Then, we propose two algorithms for computing the square roots of the -circulant matrix and the skew -circulant matrix, respectively. In particular, we show that the square roots of the -circulant matrix are still -circulant matrices. Both the theoretical analysis and the numerical experiments show that our algorithms are faster than the standard Schur method.
"A Note on the Square Roots of a Class of Circulant Matrices." J. Appl. Math. 2013 1 - 6, 2013. https://doi.org/10.1155/2013/601243