SYMMETRIC MATRIX PENCILS: CODIMENSION COUNTS AND THE SOLUTION OF A PAIR OF MATRIX EQUATIONS

Full text
Author(s):	Dmytryshyn, Andrii ^{[1, 2]} ; Kagstrom, Bo ^{[1, 2]} ; Sergeichuk, Vladimir V. ^[3] Total Authors: 3
Affiliation:	^[1] Umea Univ, Dept Comp Sci, SE-90187 Umea - Sweden ^[2] Umea Univ, HPC2N, SE-90187 Umea - Sweden ^[3] Ukrainian Acad Sci, Inst Math, Kiev - Ukraine Total Affiliations: 3
Document type:	Journal article
Source:	ELECTRONIC JOURNAL OF LINEAR ALGEBRA; v. 27, p. 1-18, JAN 2014.
Web of Science Citations:	6
Abstract
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. (AU)

FAPESP's process:	12/18139-2 - Methods of representation theory in linear algebra
Grantee:	Vyacheslav Futorny
Support Opportunities:	Research Grants - Visiting Researcher Grant - International