Classification problems for matrices, matrix spaces and tensors

• Grant number: 18/24089-4
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: July 01, 2019
• End date: June 30, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Vyacheslav Futorny
• Grantee: Vyacheslav Futorny
• Visiting researcher: Volodymyr 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

Abstract

This is a research project in the area of Linear Algebra. The main problems to be studies are: classification of the systems of tensors of order r, study of matrix pencils, the canonical form of pair of nilpotent commutative operators and vector spaces of matrices with respect to congruence. (AU)

Scientific publications

(7)

(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)

BELITSKII, GENRICH R.; FUTORNY, VYACHESLAV; MUZYCHUK, MIKHAIL; SERGEICHUK, VLADIMIR V.. Congruence of matrix spaces, matrix tuples, and multilinear maps. Linear Algebra and its Applications, v. 609, p. 15-pg., 2021-01-15. (18/24089-4, 18/23690-6)

FUTORNY, VYACHESLAV; KLYMCHUK, TETIANA; KLYMENKO, OLENA; SERGEICHUK, VLADIMIR V.; SHVAI, NADIYA. Perturbation theory of matrix pencils through miniversal deformations. Linear Algebra and its Applications, v. 614, p. 45-pg., 2021-02-02. (18/24089-4)

FUTORNY, VYACHESLAV; KLYMCHUK, TETIANA; KLYMENKO, OLENA; SERGEICHUK, VLADIMIR V.; SHVAI, NADIYA. Perturbation theory of matrix pencils through miniversal deformations. Linear Algebra and its Applications, v. 614, n. SI, p. 455-499, APR 1 2021. (18/24089-4)

CAALIM, V, JONATHAN; FUTORNY, VYACHESLAV; SERGEICHUK, VLADIMIR V.; TANAKA, YU-ICHI. Isometric and selfadjoint operators on a vector space with nondegenerate diagonalizable form. Linear Algebra and its Applications, v. 587, p. 92-110, FEB 15 2020. (18/24089-4, 18/23690-6)

BORGES, VICTOR SENOGUCHI; KASHUBA, IRYNA; SERGEICHUK, VLADIMIR V.; SODRE, EDUARDO VENTILARI; ZAIDAN, ANDRE. Classification of linear operators satisfying (Au, v) = (u, A(r)v) or (Au, A(r)v) = (u, v) on a vector space with indefinite scalar product. Linear Algebra and its Applications, v. 611, p. 118-134, FEB 15 2021. (18/24089-4)

BONDARENKO, VITALIJ M.; FUTORNY, VYACHESLAV; PETRAVCHUK, ANATOLII P.; SERGEICHUK, VLADIMIR V.. Pairs of commuting nilpotent operators with one-dimensional intersection of kernels and matrices commuting with a Weyr matrix. Linear Algebra and its Applications, v. 612, p. 188-205, MAR 1 2021. (18/24089-4, 18/23690-6)

BOVDI, VICTOR A.; KLYMCHUK, TETIANA; RYBALKINA, TETIANA; SALIM, MOHAMED A.; SERGEICHUK, VLADIMIR V.. Operators on positive semidefinite inner product spaces. Linear Algebra and its Applications, v. 596, p. 82-105, JUL 1 2020. (18/24089-4)