Estimation of Linear Projection

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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.