  Let $\mathcal A:U\to V$ be a linear mapping between vector spaces $U$ and $V$
over a field or skew field $\mathbb F$ with symmetric, or skew-symmetric, or
Hermitian forms $\mathcal B:U\times U\to\mathbb F$ and $\mathcal C:V\times
V\to\mathbb F.$ We classify the triples $(\mathcal A,\mathcal B,\mathcal C)$ if
$\mathbb F$ is $\mathbb R$, or $\mathbb C$, or the skew field of quaternions
$\mathbb H$. We also classify the triples $(\mathcal A,\mathcal B,\mathcal C)$
up to classification of symmetric forms and Hermitian forms if the
characteristic of $\mathbb F$ is not 2.
