If I multiply a Hurwitz matrix (real part of eigenvalues are negative) with a diagonal positive definite matrix, does the product still remain as Hurwitz matrix?
2025-01-13 05:28:06.1736746086
Is a product of a Hurwitz matrix and a diagonal positive definite matrix always Hurwitz?
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How about $$A=\pmatrix{1&1\\-4&-3}$$ and $$B=\pmatrix{4&0\\0&1}.$$ Then $A$ has repeated eigenvalues $-1$ so is Hurwitz, but $BA$ has positive trace so isn't.