  Let $\{X(t) : t \in \mathbb{R}^d \}$ be a multivariate operator-self-similar
random field with values in $\mathbb{R}^m$. Such fields were introduced in [24]
and satisfy the scaling property $\{X(c^E t) : t \in \mathbb{R}^d \}
\stackrel{\rm d}{=} \{c^D X(t) : t \in \mathbb{R}^d \}$ for all $c > 0$, where
$E$ is a $d \times d$ real matrix and $D$ is an $m \times m$ real matrix. We
solve an open problem in [24] by calculating the Hausdorff dimension of the
range and graph of a trajectory over the unit cube $K = [0,1]^d$ in the
Gaussian case. In particular, we enlighten the property that the Hausdorff
dimension is determined by the real parts of the eigenvalues of $E$ and $D$ as
well as the multiplicity of the eigenvalues of $E$.
