Putting this out to invoke Cunningham's Law... my intuition says that while the article may be right about matrices in the real numbers, using the eigenvalues to check for closeness to singularity may be more valid on the floats, because probably what you're testing for isn't "closeness to singularity" but how close you are to having floating point failures, and that seems at least likely to be heavily correlated.
I now sit back and wait for someone to explain why this is wrong while I act like this was an entirely unanticipated result of my post.
Putting this out to invoke Cunningham's Law... my intuition says that while the article may be right about matrices in the real numbers, using the eigenvalues to check for closeness to singularity may be more valid on the floats, because probably what you're testing for isn't "closeness to singularity" but how close you are to having floating point failures, and that seems at least likely to be heavily correlated.
I now sit back and wait for someone to explain why this is wrong while I act like this was an entirely unanticipated result of my post.