what linear algebra do you use most often for practical problems?
Raplh: I'm not in software, but rather algorithm development for determining radio positions (like GPS but including other methods for cell phones).  I have used eigenanalysis a number of times, a lot of orthogonal basis shifting of various kinds, implicilty a lot of matrix inversions and pseudoinversions to solve things.  I do most of my R&D using matlab, and have learned a lot of linear algebra reading their helpfiles.  I use hilbert spaces and what I learned about them 30 years ago almost constantly.