I'm trying to find information on the eigenvalues of an n×n matrix $A$ such that

$A=D+J$ Where $D$ is some complex valued diagonal matrix, and $J$ is a rank one matrix, $J = uu^T$. How to compute the eigen values of $A$ in this case?

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I'm trying to find information on the eigenvalues of an n×n matrix $A$ such that

$A=D+J$ Where $D$ is some complex valued diagonal matrix, and $J$ is a rank one matrix, $J = uu^T$. How to compute the eigen values of $A$ in this case?

generalrank-$1$ matrix (which would be of the form $J = uv^T$ rather than $J = uu^T$), or do you really wish $J$ to be of the form $J = uu^T$ (and thus symmetric)? $\endgroup$