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Post Closed as "Not suitable for this site" by Joseph Van Name, YCor, Vladimir Dotsenko, M.G., Gro-Tsen
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kjetil b halvorsen
kjetil b halvorsen
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multiplication Multiplication of a symmetric matrixesmatrices

I'm wonder if the next claim is true or not: 
If A,B is a symmetric matrixesmatrices over the real numbers, and A is PSD , B is PD implies than AB is PSD. PD - positive defineddefinite
PSD - positive semidefinite 
If it is true , how can i prove it? and if it wrong , I wonder if there is some examples that shows that. Thanks a lot.

multiplication of a symmetric matrixes

I'm wonder if the next claim is true or not: If A,B is a symmetric matrixes over the real numbers, and A is PSD , B is PD implies than AB is PSD. PD - positive defined PSD - positive semidefinite If it is true , how can i prove it? and if it wrong , I wonder if there is some examples that shows that. Thanks a lot.

Multiplication of a symmetric matrices

I'm wonder if the next claim is true or not: 
If A,B is a symmetric matrices over the real numbers, and A is PSD , B is PD implies than AB is PSD. PD - positive definite
PSD - positive semidefinite 
If it is true , how can i prove it? and if it wrong , I wonder if there is some examples that shows that.

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GKR
GKR
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multiplication of a symmetric matrixes

I'm wonder if the next claim is true or not: If A,B is a symmetric matrixes over the real numbers, and A is PSD , B is PD implies than AB is PSD. PD - positive defined PSD - positive semidefinite If it is true , how can i prove it? and if it wrong , I wonder if there is some examples that shows that. Thanks a lot.