If column vectors of ${\bf B}$ are independent and normalized, can we conclude the row summation of $({{\bf B}^T{\bf B}})^{-1}$ nonnegative? By row summation, I mean $({{\bf B}^T{\bf B}})^{-1}{\bf 1}$. ${\bf 1}$ is a vector with components all one's.
Sorry for this question. Seems what I need is only ${\bf 1}^T({\bf B}^T{\bf B}){\bf 1}>0$. But this is trivial.
Thank you all so much!