Symmetric matrix pencils: codimension counts and the solution of a pair of matrix equations

Dmytryshyn, Andrii,1986-Umeå universitet,Institutionen för datavetenskap,Högpresterande beräkningscentrum norr (HPC2N) (author)

Symmetric matrix pencils : codimension counts and the solution of a pair of matrix equations

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.

Kågström, Bo,1948-Umeå universitet,Institutionen för datavetenskap,Högpresterande beräkningscentrum norr (HPC2N),UMIT(Swepub:umu)boka0002 (author)
Sergeichuk, Vladimir V.Ukrainian Acad Sci, Kiev, Ukraine (author)
Umeå universitetInstitutionen för datavetenskap (creator_code:org_t)

In:The Electronic Journal of Linear Algebra: University of Wyoming Libraries27, s. 1-181537-95821081-3810

By the author/editor: Dmytryshyn, Andr ...; Kågström, Bo, 19 ...; Sergeichuk, Vlad ...

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NATURAL SCIENCES: NATURAL SCIENCES; and Mathematics; and Algebra and Logi ...

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