$A$ and $B$ are two symmetric and PSD matrices. Also,
$B = A + ee^T$.
How can one prove that $\operatorname{null}(B) \subset \operatorname{null}(A)$?
$A$ and $B$ are two symmetric and PSD matrices. Also,
$B = A + ee^T$.
How can one prove that $\operatorname{null}(B) \subset \operatorname{null}(A)$?
Hint: look at $x^tBx=x^tAx+x^tee^tx$, where $x$ is such that $Bx=0$.