Let $\cal A$ and $\cal B$ 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 $\cal A$ is transformed to $\cal B$ by homeomorphisms within $\mathbb C^{ n_1},\dots,\mathbb C^{ n_t}$ if and only if $\cal A$ is transformed to $\cal B$ by linear bijections within $\mathbb C^{ n_1},\dots,\mathbb C^{ n_t}$.
Categories: math.RT math.RA