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If $A>0$ , $B>0$

what are conditions on $A , B$ to conclude $AB>0$.

hadi.reisizadeh
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  • Positive definite means for a matrix $A$, it's positive definite if $xAx>0$ for all possible values for the vector $x$. – Connor James Feb 21 '16 at 20:01
  • If $A>0$ and $B>0$? No additional conditions! The sum of positive numbers multiplied with positive numbers will be positive... – Jeremias K Feb 21 '16 at 20:02
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    @JeremiasK The tag positive-definite rather suggests this is not about entry-positive matrices... –  Feb 21 '16 at 20:04
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    Does your definition of positive definiteness include symmetry/hermitian? – user251257 Feb 21 '16 at 20:08

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