I'm going through Andrew Ng's notes on ICA and the blind source separation example mostly makes sense. In essence, we have $d$ microphone recordings $x \in R^d$ and also $d$ independent speakers in $s \in R^d$, represented with $x = As$, where we want to recover the mixing matrix $A$ and source coefficients $s$ from observations $x$. However, what happens if $x$ and $s$ are not the same dimension, i.e $c$ recordings of $d$ speakers. Does this still make sense? And is this still tractable since A is now non square, $A \in R^{c \times d}$, so the system is undetermined with $c < d$?
Also on a tangent, is $A$ analagous to the matrix of principal components in PCA, $V$?
