I have the problem in the following form $C=AX(BX)^\dagger$ where $\dagger$ indicates pseudoinverse.
$dim(A)=M, N$
$dim(B)=P, N$
$dim(X)=N, K$
with $M>N>K$ and $P>N>K$
All abovementioned matrices have a full rank. The resulting matrix $C$ has the dimentionality of $M, P$, but it is rank deficient $rank(C) \leq K$. How could I express which exactly rows/columns of $C$ became linearly dependent?
I know that SVD would give me the singular values indicating rank of $C$. Zero entries would indicate that some of the rows/columns are linearly dependent. However, I am not able to trace those zero entries back in order to find the linearly dependent rows/columns.