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pro vyhledávání: '"van Straaten, M"'
We extend Theorem 1 of R. Reams, A Galois approach to m-th roots of matrices with rational entries, LAA 258 (1997), 187-194. Let $p(\lambda)$ be any polynomial over $\mathbb{Q}$ and let $A\in M_n(\mathbb{Q})$ have irreducible characteristic polynomia
Externí odkaz:
http://arxiv.org/abs/2307.06303
In this paper we will look at the well known interlacing problem, but here we consider the result for Hermitian matrices in the Minkowski space, an indefinite inner product space with one negative square. More specific, we consider the $n\times n$ ma
Externí odkaz:
http://arxiv.org/abs/2212.00319
Publikováno v:
In Linear Algebra and Its Applications 15 July 2024 693:236-247
Polar decompositions of quaternion matrices with respect to a given indefinite inner product are studied. Necessary and sufficient conditions for the existence of an $H$-polar decomposition are found. In the process an equivalent to Witt's theorem on
Externí odkaz:
http://arxiv.org/abs/2106.10527
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 given $H$-selfadjoint quaternion matrix. In the process, when such an
Externí odkaz:
http://arxiv.org/abs/2106.05072
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.
Externí odkaz:
http://arxiv.org/abs/2007.13396
Publikováno v:
In Linear Algebra and Its Applications 15 May 2023 665:107-138
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Publikováno v:
In Linear Algebra and Its Applications 15 July 2021 621:29-49
Publikováno v:
In Linear Algebra and Its Applications 1 February 2021 610:804-826