Sorting singular values

[>flo<]

Today in class we discussed assignment 2, problem 2 and we talked about sorting the singular values / eigenvalues before computing the cumulative variance. I just noticed that this is actually not necessary.

The singular values on the diagonal of S (let X = USV) should already be sorted.

From my ML notes:

[...]
All diagonal elements of S are non-negative and in non-increasing order:
s_1 >= s_2 >= ... s_p >= 0
where p = min(n,m)

[sroth]

I thought I mentioned that they were already sorted... Sorry, if I didn't!
But anyway, the reason why I made this comment about sorting was that when I gave out this assignment before, some students changed the sorting to increasing order instead of keeping the decreasing order (for whatever reason), and then got wrong results.

Thanks for pointing this out,
SR