  Let $V$ be a vector space over a field $\mathbb F$ with scalar product given
by a nondegenerate sesquilinear form whose matrix is diagonal in some basis. If
$\mathbb F=\mathbb C$, then we give canonical matrices of isometric and
selfadjoint operators on $V$ using known classifications of isometric and
selfadjoint operators on a complex vector space with nondegenerate Hermitian
form. If $\mathbb F$ is a field of characteristic different from $2$, then we
give canonical matrices of isometric, selfadjoint, and skewadjoint operators on
$V$ up to classification of symmetric and Hermitian forms over finite
extensions of $\mathbb F$.
