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$H + H^T$ is a positive definite matrix and $P$ is also a positive definite matrix.

Will $Q = PH + H^TP$ be a positive definite matrix?

In my calculations, it is not positive definite. But I read a paper saying that $Q$ should be positive definite. Is it so?

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    Nobody's ever done that before! @Fatima, the place you just posted this question is the _meta_ site, which is for discussion of the main site, not for discussion of mathematics.2011-08-09
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    @Qiaochu: If you mean nobody's posted a math question on meta, it happened once before: http://math.stackexchange.com/questions/33394/prime-numbers-which-solve-2s-1mod-p2011-08-09
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    @Jonas: my apologies. I should have been more precise: I've never seen anyone do that before!2011-08-09
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    Fatima: What calculations, and what paper?2011-08-09
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    @Jonas: paper is "A new approach to the LQ design from the viewpoint of the inverse regulator problem" by Takao Fujii2011-08-09
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    @Qiachu: I am extremely sorry if I posted my question in wrong place. I am not familiar of this system. This is my second question.2011-08-09

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