Methods of representation theory in linear algebra

• Grant number: 12/18139-2
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: February 01, 2013
• End date: January 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Vyacheslav Futorny
• Grantee: Vyacheslav Futorny
• Visiting researcher: Vladimir Sergeichuk
• Visiting researcher institution: National Academy of Sciences of Ukraine (NASU), Ukraine
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 10/50347-9 - Algebras, representations e applications, AP.TEM

Abstract

We plan to address classification problems of systems of forms and linear mappings considering them as representations of mixed graphs, and systems of linear and semilinear mappings on linear or unitary spaces considering them as representations of biquivers. (AU)

Scientific publications

(6)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

DMYTRYSHYN, ANDRII; FUTORNY, VYACHESLAV; SERGEICHUK, VLADIMIR V.. Miniversal deformations of matrices under {*}congruence and reducing transformations. Linear Algebra and its Applications, v. 446, p. 388-420, APR 1 2014. (10/50347-9, 10/07278-6, 12/18139-2)

DMYTRYSHYN, ANDRII; KAGSTROM, BO; SERGEICHUK, VLADIMIR V.. SYMMETRIC MATRIX PENCILS: CODIMENSION COUNTS AND THE SOLUTION OF A PAIR OF MATRIX EQUATIONS. ELECTRONIC JOURNAL OF LINEAR ALGEBRA, v. 27, p. 1-18, JAN 2014. (12/18139-2)

FUTORNY, VYACHESLAV; RYBALKINA, TETIANA; SERGEICHUK, VLADIMIR V.. Regularizing decompositions for matrix pencils and a topological classification of pairs of linear mappings. Linear Algebra and its Applications, v. 450, p. 121-137, JUN 1 2014. (10/50347-9, 12/18139-2)

RYBALKINA, T. V.; SERGEICHUK, V. V.. Topological Classification of the Oriented Cycles of Linear Mappings. UKRAINIAN MATHEMATICAL JOURNAL, v. 66, n. 10, p. 1575-1581, MAR 2015. (12/18139-2)

DMYTRYSHYN, ANDRII; FUTORNY, VYACHESLAV; SERGEICHUK, VLADIMIR V.. Miniversal deformations of matrices under *congruence and reducing transformations. Linear Algebra and its Applications, v. 446, p. 33-pg., 2014-04-01. (10/50347-9, 12/18139-2, 10/07278-6)

DMYTRYSHYN, ANDRII; FUTORNY, VYACHESLAV; KAGSTROM, BO; KLIMENKO, LENA; SERGEICHUK, VLADIMIR V.. Change of the congruence canonical form of 2-by-2 and 3-by-3 matrices under perturbations and bundles of matrices under congruence. Linear Algebra and its Applications, v. 469, p. 305-334, MAR 15 2015. (10/50347-9, 12/18139-2)