  It has been shown that if $T$ is a complex matrix, then {\small\begin{align*}
\omega(T)&=\frac{1}{n}\sup\left\{|\mathrm{Tr}\ X|;\ X\in W^n(T)\right\}\\
&=\frac{1}{n}\sup\left\{\|X\|_1;\ X\in W^n(T)\right\}\\ &= \sup\left\{
\omega(X);\ X\in W^n(T)\right\} \end{align*} }
  where $n$ is a positive integer, $\omega(T)$ is the numerical radius and
$W^n(T)$ is the $n$'th matricial range of $T$.
