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Let A and B be two positive definite matrices.Then is it true that A+B is also positive definite? My view:I have taken several examples and every time it indicates that A+B is p.d.But haven't able to prove it explicitly.Anybody please help.

user1991
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1 Answers1

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Yes, it is true. Note that for any vector $x \neq 0$, we have $$ x^T(A + B)x = x^TAx + x^TBx > 0 $$

Ben Grossmann
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