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Symmetric matrix pencils: codimension counts and the solution of a pair of matrix equations
Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N).
Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, High Performance Computing Center North (HPC2N). (UMIT)
Ukrainian Acad Sci, Kiev, Ukraine.
2014 (English)In: The Electronic Journal of Linear Algebra, ISSN 1537-9582, E-ISSN 1081-3810, Vol. 27, 1-18 p.Article 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, 1-18 p.
Keyword [en]
Pair of symmetric matrices, Matrix equations, Orbits, Codimension
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-87046ISI: 000331236500001OAI: oai:DiVA.org:umu-87046DiVA: diva2:708978
Funder
eSSENCE - An eScience CollaborationSwedish Research Council, A0581501
Available from: 2014-03-31 Created: 2014-03-18 Last updated: 2017-12-05Bibliographically approved

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