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

Autor(es)

Dmytryshyn, Andrii ^{[1, 2]} ; Kagstrom, Bo ^{[1, 2]} ; Sergeichuk, Vladimir V. ^[3]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: ELECTRONIC JOURNAL OF LINEAR ALGEBRA; v. 27, p. 1-18, JAN 2014.
• Citações Web of Science: 6

Resumo

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)

• Processo FAPESP: 12/18139-2 - Métodos de teoria de representações em álgebra linear
• Beneficiário: Vyacheslav Futorny
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional