  Assume $\N$ is a von Neumann algebra of type II$_1$ with a tracial state
$\tau_{\N}$, and $\M$ is the von Neumann algebra of the $n\times n$ matrices
over $\N$ with the canonical tracial state $\tau_{\M}$. Let $\mathcal D_n$ be
the subalgebra of $\M$ consisting of scalar diagonal matrices in $\M$. In this
article, we study the properties of semicircular elements in $\M$ that are free
from $\mathcal D_n$ with respect to $\tau_{\M}$. Then we define a new concept
"matricial distance" of two elements in $\M$ and compute the matricial distance
between two free semicircular elements in $\M$.
