65F: Numerical linear algebra
Numerical linear algebra topics include: solutions of linear systems AX = B, eigenvalues and eigenvectors, matrix factorizations.
This image slightly hand-edited for clarity.
Browse all (old) classifications for this area at the AMS.
There is a substantial pool of information on numerical issues in linear algebra available on the internet -- see for example the newsgroup sci.math.num-analysis.
Note that mathematical algorithms constitute one of the most web-accessible bodies of human knowledge available. A search at one of these sites can easily save considerable programming headaches! Highly recommended are NETLIB and GAMS. See also TOMS.