How to find a positive semidefinite matrix $Y$ such that $YB =0$ where $B$ is given $B$ is an $n\times m$ matrix, $m\leq n$.
I have to find an $n\times n$ positive semidefinite matrix $Y$ such that $YB = 0$. 
Please help me figure out how can I find the matrix $Y$.

I can give you the answer in the case $m=n$. 


*

*if $\det(B)\neq 0$ then $B$ is invertible, and therefore the only matrix $Y$ is $Y=0$.

*if $\det(B)=0$ then take $Y=adj(B)$, where $adj(B)$ is the adjugate matrix of $B$.
Oops... I forgot about the fact that $Y$ must be positive semidefinite. Sorry.
