# Checking if this matrix is Positive Semdefinite?

For a matrix $A \in \mathbb R^{m\times n}$ with columns $a_i \in \mathbb R^m$, we know that $A^\top A$ is Positive Semidefinite (PSD).

I am interested in checking if B is positive semidefinite where $B_{ij} = (a_i^\top a_j)^2$. Each component of $B$ is the square of corresponding component of $A^\top A$.

• if $A^\top A$ is diagonal it's obviiously trivial, as a feel I think that you can't conclude nothing in general, but I'm curious to see tha aswers to this question – gimusi Dec 5 '17 at 0:33