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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

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  • $\begingroup$ What does $\delta_{\lambda_i}$ mean? $\endgroup$
    – Marcel
    Apr 20, 2016 at 12:29
  • $\begingroup$ It's mean : $$ \delta_{\lambda_i}(x) = \begin{cases} 1, & x = \lambda_i \\ 0, & x \neq \lambda_i \end{cases} $$ $\endgroup$
    – Brandon
    Apr 20, 2016 at 13:59

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