I saw few questions about it, but still can't understand.
Let $A$ be a symmetric matrix and $\lambda_{\max}$ its largest eigenvalue. Is the following true for all $A$?
$$
\lambda_{\max} \ge a_{ii} \forall i
$$
That is, is the largest eigenvalue of a symmetric matrix always greater than any of its diagonal entries?
Is it somehow related to spectral radius and the following equation?
$$
\rho(A)=\max|\lambda_i|.
$$
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