Given a fixed symmetric matrix $S$, can one change the spectrum of $S$ to any desired set of eigenvalues $\{\lambda_1,\dots,\lambda_n\}$ by adding a diagonal matrix $D$ to $S$?
Changing the spectrum of a symmetric matrix by diagonal perturbations
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linear-algebra
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0Unfortunately not. – 2011-10-18
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0For a special case take a look at [this](http://math.stackexchange.com/questions/56771/) – 2011-10-18