On the Right Eigenvalues of the Quaternionic Matrix Polynomials

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Autori principali:	Jan, Ovaisa, Qasim, Idrees
Natura:	Preprint
Pubblicazione:	2026
Soggetti:	Complex Variables
Accesso online:	Acceder al recurso
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_version_	1866910135021993984
author	Jan, Ovaisa Qasim, Idrees
author_facet	Jan, Ovaisa Qasim, Idrees
contents	This paper establishes new upper bounds for the right eigenvalues of monic matrix polynomials over the quaternion division algebra. The noncommutative nature of quaternion multiplication presents fundamental challenges in eigenvalue analysis, distinguishing this problem from the classical complex case. We use spectral norm inequalities for partitioned quaternionic matrices and apply them to quaternionic block matrices associated with monic matrix polynomials. By analyzing the structure of powers of these companion matrices we derive progressively sharper bounds for the right eigenvalues. Consequently, these bounds give bounds for the zeros of quaternionic polynomials.
format	Preprint
id	arxiv_https___arxiv_org_abs_2604_14813
institution	arXiv
publishDate	2026
record_format	arxiv
spellingShingle	On the Right Eigenvalues of the Quaternionic Matrix Polynomials Jan, Ovaisa Qasim, Idrees Complex Variables This paper establishes new upper bounds for the right eigenvalues of monic matrix polynomials over the quaternion division algebra. The noncommutative nature of quaternion multiplication presents fundamental challenges in eigenvalue analysis, distinguishing this problem from the classical complex case. We use spectral norm inequalities for partitioned quaternionic matrices and apply them to quaternionic block matrices associated with monic matrix polynomials. By analyzing the structure of powers of these companion matrices we derive progressively sharper bounds for the right eigenvalues. Consequently, these bounds give bounds for the zeros of quaternionic polynomials.
title	On the Right Eigenvalues of the Quaternionic Matrix Polynomials
topic	Complex Variables
url	https://arxiv.org/abs/2604.14813

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