Could someone help me, please, to understand in term of entries of a Matrix $M=(m_{i,j})_{i,j\in\{1,n\}^2}$ the following measure :
$$ \frac1{n} \sum_{i=1}^n \langle v_i,e_j \rangle \delta_{\lambda_i} $$
where, $e_j$ is the $j$-th element of the canonical base of $\mathbb{R}^n$, $\lambda_i$ the $i$-th eigenvalue of $M$, and $v_i$ the eigenvector associated to the eigenvalue $\lambda_i$.
Thank you for your attention,
Brandon