Congruence of multilinear forms

TL;DR

This paper extends a known matrix congruence result to multilinear forms, showing that certain equivalences imply congruence in a broader mathematical context.

Contribution

The paper generalizes a classical matrix congruence theorem to multilinear forms, broadening its applicability in linear algebra.

Findings

Extension of matrix congruence to multilinear forms

Conditions under which multilinear forms are congruent

Broader implications for linear algebra theory

Abstract

It is known that if A and B are two n-by-n complex matrices and (A,A^T) is simultaneously equivalent to (B,B^T), then A is congruent to B. We extend this statement to multilinear forms.