I'm trying to determine if $B^T(MM^T)B$ can be said to be positive definite or semi-positive definite. Both B and M are assumed to be made up of real numbers and are invertible.
I've read that $B^TB$ is positive definite for a real invertible matrix. (Though this may only be the case for real, invertible symmetric matrices?) And $MM^T$ (for a real invertible matrix) can be said to be semi-positive definite.
I think I saw a property that said if $MM^T$ is positive definite than $B^T(MM^T)B$ is positive definite but I cannot find where I read that or how $MM^T$ being semi-positive definite would change things.