LAUSR

Abstract Two matrix vector spaces V , W ⊂ C n × n are said to be equivalent if S V R = 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 × … × 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 φ 1 , … , φ k : U → U ′ and ψ : V → V ′ that transforms F to G , then there exists such a set with φ 1 = … = φ k .