F. Theron

activity

20202022

collaborators

4 papers

math.FA2022

Solutions of the matrix equation $p (X) = A$ , with polynomial function $p (λ)$ over field extensions of $Q$

Gilbert Groenewald, Dawie Janse van Rensburg, Andre Ran +2

Let $H$ be a field with $Q \subset H \subset C$ , and let $p (λ)$ be a polynomial in $H [λ]$ , and let $A \in H^{n \times n}$ be nonderog…

math.FA2021

$m$ th roots of $H$ -selfadjoint matrices over the quaternions

D. B. Janse van Rensburg, A. C. M. Ran, F. Theron +1

The complex matrix representation for a quaternion matrix is used in this paper to find necessary and sufficient conditions for the existence of an $H$ -selfadjoint $m$ th root of a…

math.RA2020

Square roots of H-nonnegative matrices

Dawie B. Janse van Rensburg, Madelein van Straaten, Frieda Theron +1

Roots of matrices are well-studied. The conditions for their existence are understood: The block sizes of nilpotent Jordan blocks, arranged in pairs, have to satisfy some simple al…

math.FA2020

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

G. J. Groenewald, D. B. Janse van Rensburg, A. C. M. Ran +2

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…

Solutions of the matrix equation p(X)=A, with polynomial function p(λ) over field extensions of Q

mth roots of H-selfadjoint matrices over the quaternions

Square roots of H-nonnegative matrices

mth roots of H-selfadjoint matrices

Solutions of the matrix equation $p (X) = A$ , with polynomial function $p (λ)$ over field extensions of $Q$

$m$ th roots of $H$ -selfadjoint matrices over the quaternions

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