Answer by Elias for Positive definiteness of product of symmetric positive...
Let $C=AB$ and $D=\frac{C+C^T}{2}$. Even though $C$ is not symmetric, $D$ is. Moreover, $x^TCx=x^TDx$. So a sufficient condition for $C$ to be positive definite is that $x^TDx>0$ for all nonzero...
View ArticlePositive definiteness of product of symmetric positive definite matrices
Suppose $A,B$ are symmetric and positive definite (real) matrices such that $AB$ is not symmetric (equivalently $AB\neq BA$). My question is, what are sufficient and/or necessary conditions for $AB$...
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