Given a linear system:
$Y=AX+W$
Where:
$X$ is the input signal of size $N \times K$
$Y$ is the output signal of size $M \times K$
$A$ is a projection of size $M\times N$; with $M >> N$
$W$ is i.i.d Gaussian noise
Now, assume that we know X and Y and the projection A is estimated by:
$A \approx YX^{T}$
Could you tell me the relationship between K and N for a good estimation of A ?
P/S: I read in a textbook which said that we should have $K \geq N $, but I don't know why.
Thank you very much.