3 ms·

What was the noise cancelling project? How did you use this fact to cancel noise?

• sdenton4 3y ago
  Just guessing, but.... A common noise cancellation technique is to throw away small eigenvalues, as in PCA. This result relates eigenvalues to the structure of the matrix, so might be helpful for reducing ev's without bothering with diagonalization? [Edit] This would presumably involve just zeroing out the rows with small diagonal elements and small-ish off-diagonal norm... Center the eigenvalue estimate disk at zero, and then zero out the rest of the row to make the estimate exact.
  • sdenton4 3y ago
    (and after one more thought about it, one would zero out the row /and column/ to preserve the symmetry of the matrix, if applicable, and thus keep the eigenvalues real. and one would probably want to think a bit about whether this kind of deletion actually makes sense for the problem... doing real PCA isn't /that/ hard in most cases - I think I would do something this janky only for extremely large matrices or for realtime operation on a microcontroller or something, and then only after thinking hard about it.)