$m$th roots of $H$-selfadjoint matrices

TL;DR

This paper establishes conditions for the existence of $H$-selfadjoint $m$th roots of matrices and provides a construction method when such roots exist, advancing understanding of matrix roots in indefinite inner product spaces.

Contribution

It offers necessary and sufficient conditions for $H$-selfadjoint $m$th roots and presents a construction method, filling a gap in matrix root theory for indefinite inner product spaces.

Findings

Characterization of existence conditions for $H$-selfadjoint $m$th roots.

Explicit construction method for these roots when they exist.

Enhanced understanding of matrix roots in indefinite inner product spaces.

Abstract

In this paper necessary and sufficient conditions are given for the existence of an $H$-selfadjoint $m$th root of a given $H$-selfadjoint matrix. A construction is given of such an $H$-selfadjoint $m$th root when it does exist.