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Symmetric matrix pencils: codimension counts and the solution of a pair of matrix equations
Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden.ORCID iD: 0000-0001-9110-6182
Department of Computing Science and HPC2N, Umeå University, Umeå, Sweden.
Ukrainian Acad Sci, Kiev, Ukraine.
2014 (English)In: The Electronic Journal of Linear Algebra, ISSN 1537-9582, E-ISSN 1081-3810, Vol. 27, p. 1-18Article in journal (Refereed) Published
Abstract [en]

The set of all solutions to the homogeneous system of matrix equations (X-T A + AX, X-T B + BX) = (0, 0), where (A, B) is a pair of symmetric matrices of the same size, is characterized. In addition, the codimension of the orbit of (A, B) under congruence is calculated. This paper is a natural continuation of the article [A. Dmytryshyn, B. Kagstrom, and V. V. Sergeichuk. Skew-symmetric matrix pencils: Codimension counts and the solution of a pair of matrix equations. Linear Algebra Appl., 438:3375-3396, 2013.], where the corresponding problems for skew-symmetric matrix pencils are solved. The new results will be useful in the development of the stratification theory for orbits of symmetric matrix pencils.

Place, publisher, year, edition, pages
2014. Vol. 27, p. 1-18
Keywords [en]
Pair of symmetric matrices, Matrix equations, Orbits, Codimension
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:oru:diva-74896DOI: 10.13001/1081-3810.1602ISI: 000331236500001Scopus ID: 2-s2.0-84894423199OAI: oai:DiVA.org:oru-74896DiVA, id: diva2:1332891
Funder
eSSENCE - An eScience CollaborationSwedish Research Council, A0581501Available from: 2019-06-28 Created: 2019-06-28 Last updated: 2019-09-20Bibliographically approved

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Dmytryshyn, AndriiKågström, Bo

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