Are people interested enough in this for a blog post? I studied numerical analysis and would be happy to post some of the basics if people are interested.
We can all count the floating-point operations, and today caches sometimes influence matrix algorithms more than raw flop counts. The problem gets more interesting when the matrix becomes ill conditioned and different algorithms will produce very different results.
Side note: My professor also mentioned it at least 3 times in each lecture... so it is important.