Computing the square roots of matrices with central symmetry

Computing the square roots of matrices with central symmetry

For computing square roots of a nonsingular matrix A, which are functions of A, two well known fast and stable algorithms, which are based on the Schur decomposition of A, were proposed by Björk and Hammarling [3], for square roots of general complex matrices, and by Higham [10], for real square roots of real matrices. In this paper we further consider (the computation of) the square roots of m...

On square roots and norms of matrices with symmetry

The present work concerns the algebra of semi-magic square matrices. These can be decomposed into matrices of specific rotational symmetry types, where the square of a matrix of pure type always has a particular type. We examine the converse problem of categorising the square roots of such matrices, observing that roots of either type occur, but only one type is generated by the functional calc...

Computing the Square Roots of a Class of Circulant Matrices

On computing complex square roots of real matrices

We present an idea for computing complex square roots of matrices using only real arithmetic.

Hamiltonian Square Roots of Skew-Hamiltonian Matrices

We present a constructive existence proof that every real skew-Hamiltonian matrix W has a real Hamiltonian square root. The key step in this construction shows how one may bring any such W into a real quasi-Jordan canonical form via symplectic similarity. We show further that every W has infinitely many real Hamiltonian square roots, and give a lower bound on the dimension of the set of all suc...