Topological classification of systems of bilinear and sesquilinear forms

Abstract

Let $\mathcal{A}$ and $\mathcal{B}$ be two systems consisting of the same vector spaces ${\mathbb{C}}^{n_1},\dots ,{\mathbb{C}}^{n_t}$ and bilinear or sesquilinear forms $A_i,B_i:{\mathbb{C}}^{n_{k(i)}}\times {\mathbb{C}}^{n_{l(i)}}\to \mathbb{C}$, for $i=1,\dots ,s$. We prove that $\mathcal{A}$ is transformed to $\mathcal{B}$ by homeomorphisms within ${\mathbb{C}}^{n_1},\dots ,{\mathbb{C}}^{n_t}$ if and only if $\mathcal{A}$ is transformed to $\mathcal{B}$ by linear bijections within ${\mathbb{C}}^{n_1},\dots ,{\mathbb{C}}^{n_t}$.

5 pages

References in corpus (1)

• Canonical forms for complex matrix congruence and *congruence