| Full text | |
| Author(s): |
Belitskii, Genrich R.
;
Futorny, Vyacheslav
;
Muzychuk, Mikhail
;
Sergeichuk, Vladimir V.
Total Authors: 4
|
| Document type: | Journal article |
| Source: | Linear Algebra and its Applications; v. 609, p. 15-pg., 2021-01-15. |
| Abstract | |
Two matrix vector spaces V,W subset of C-nxn are said to be equivalent if SVR =W for some nonsingular S and R. These spaces are congruent if R= S-T. We prove that if all matrices in V and W are symmetric, or all matrices in V and W are skew-symmetric, then V and W are congruent if and only if they are equivalent. Let F : U x ... xU -> V and G : U' x ... x U' -> V' be symmetric or skew-symmetric k-linear maps over C. If there exists a set of linear bijections phi(1), ..., phi(k) : U -> U' and psi : V -> V' that transforms F to G, then there exists such a set with phi(1) = ... = phi(k). (C) 2020 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 18/24089-4 - Classification problems for matrices, matrix spaces and tensors |
| Grantee: | Vyacheslav Futorny |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |
| FAPESP's process: | 18/23690-6 - Structures, representations, and applications of algebraic systems |
| Grantee: | Ivan Chestakov |
| Support Opportunities: | Research Projects - Thematic Grants |