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I'm stuck on finding the eigenvalues of $$ \bar{A} = \begin{bmatrix} 0 & S\\ S^\top & A \end{bmatrix} $$ Both $S$ and $A$ are square matrices of the same dimension and are invertible. $A$ is symmetric positive definite.

Any help is appreciated. :-D

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    I'm afraid not much can be said in such generality. Do you know *anything* about those matrices?2011-12-07
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    This isn't what's usually referred to as a block triangular matrix -- that would mean that the off-diagonal block is zero, not the diagonal block.2011-12-07
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    A better description might be that your matrix is "block antitriangular". In any event, is $\mathbf A$ (the $2,2$ block) symmetric?2011-12-07
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    hmm, in my problem $A$ is symmetric positive definite.2011-12-07
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    You should have mentioned that to begin with, you know.2011-12-07

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