I have the following matrix: $$G = \left[ \begin{array}{cc} A & e \\ e^T & 0 \end{array} \right]$$
Where $A = BB^T$ is symmetric, positive semi-definite, and $e = [1,1,...,1]^T$. let says $A$ is $n \times n$ and $e$ is $n \times 1$.
Is matrix $G$ a nonsingular matrix ? Why?
My question is from the stanford lecture: https://see.stanford.edu/materials/lsocoee364a/hw8sol.pdf
The prof says the KKT matrix is nonsingular, if it satisfies one of four conditions.
Is there any matrix $Q$ such that $A$ + $eQe^T > 0$ like the prof's fourth condition
Thanks.