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Is it possible to demonstrate that the complex eigenvalues of the generalised eigenvalue problem $Ax=\lambda B x$ have positive real parts if we know that both $A$ and $B$ have complex eigenvalues with positive real parts?

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closed as off-topic by Silvia Ghinassi, Daniel W. Farlow, Siminore, 3SAT, choco_addicted Mar 1 '16 at 17:41

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The answer is no. As a counterexample, take $$ A = \pmatrix{1&10\\0&1}, B = \pmatrix{1&0\\10&1} $$ note that $A^{-1}B$ has eigenvalues with negative real part.

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