I have the following LMI (linear matrix inequality):
$F^TP+PF\leq 0$ where $P$ is a positive definite matrix.
if I have the following condition $Q\leq P$, $Q$ is a positive definite matrix.
is it right to write the LMI as $F^TQ+QF\leq 0$ ?
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Martin Sleziak
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What do you mean by $Q \leq P$ ? You have a norm on $M_n$ that allows you to say so ? – Thinking Sep 18 '18 at 22:31
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By $\geq$, do you mean $succeq$, the ordering of matrices with respect to the cone of positive semidefinite matrices? Or, do you mean elementwise inequality? – Brian Borchers Sep 18 '18 at 22:33
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$Q-P \leq 0$ is negative definite all the eigenvalue of $Q-P$ are negatives – khallouq abdelmounaim Sep 18 '18 at 22:48
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The same question on MathOverflow: linear matrix inequiality. I think that this answer gives a very reasonable advice on cross-posting. Of course, other posts tagged ([meta-tag:cross-posting]) on meta might be worth having a look. – Martin Sleziak Sep 19 '18 at 12:34
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I answered with a counterexample at https://mathoverflow.net/questions/310932/linear-matrix-inequality – Mark L. Stone Sep 19 '18 at 19:38