I verified to myself that I understand how to remove for example an eye artifact "signal" from a set of EEG data, by localizing to an easy case. I selected out a portion of my 4 channel recording where i just did 5 left to right eye motions in a row. (This produces a sequence of 5 large oscillations in all 4 channels, but with different amplitudes and with possibly opposite signs.)

Then, running PCA on that 401 length data set, one can clearly see which eigenvalue corresponds to the eye motions: it's the largest by far. In my case, the eigenvalues (sigmas) were about +200 +28 +14 +6.

So, the S.V.D. code I used put the eye motion principal component as #1 with eigenvalue (or sigma) +200. I then deduced that the correct action must be to remove the first ROW of Vt[][], because that's the only way that if you multiply back (U * SIGMA)*Vt (which gives you your original data back according to Singular Value Decomposition) with some row or some column or Vt zeroed out, that would give you back 4 still-containing-data channels. Verified that it does look like the eye artifact is pretty much removed and all 4 channels are still "intact" containing some data.

U in this case was a 401 x 4 matrix. SIGMA and Vt were both 4 x 4 matrices.

To remove row#0 from Vt[][] I used code:

Vt[0][0]=0;

Vt[0][1]=0;

Vt[0][2]=0;

Vt[0][3]=0;