Linear algebra has never really been my strong suit (my education in college had a lot of statistical analysis, but I rarely if ever had to use linear or other higher algebra). So I apologize in advance if this is a stupid/obvious question. In any case, for work recently it is has become necessary for me to familiarize myself with singular value decomposition. Other studies on the subject have used SVD with some success, and it is fairly well established in the literature how the results turn out, and we want to compare the output of SVD directly with the output of a different computational method on the same set of matrices. Anyway, that's just the background, in case anyone was curious.
In any case, my question has to do with the numerical output of SVD. What exactly are these numbers? Are they eigenvalues/vectors? And what does it mean when some of them are negative? My grasp of SVD isn't too concrete, but I don't quite understand WHY the output would be negative?