A note on the square roots of a class of circulant matrices (Q1790027)

Summary: We prove that any \(k\)-circulant matrix and any even order skew \(k\)-circulant matrix are diagonalizable for any \(k\in\mathbb C\). 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.