Abstract
Two matrix vector spaces V,W⊂Cn×n are said to be equivalent if SVR=W for some nonsingular S and R. These spaces are congruent if R=ST. 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×…×U→V and G:U′×…×U′→V′ be symmetric or skew-symmetric k-linear maps over C. If there exists a set of linear bijections φ1,…,φk:U→U′ and ψ:V→V′ that transforms F to G, then there exists such a set with φ1=…=φk.
Original language | English |
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Pages (from-to) | 317-331 |
Number of pages | 15 |
Journal | Linear Algebra and Its Applications |
Volume | 609 |
DOIs | |
State | Published - 15 Jan 2021 |
Keywords
- Congruence
- Multilinear maps
- Weak congruence
ASJC Scopus subject areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics