Sage has many different components that may be useful for numerical analysis. In particular three packages deserve mention, they are numpy, SciPy, and cvxopt. Numpy is an excellent package that provides fast array facilities to python. It includes some basic linear algebra routines, vectorized math routines, random number generators, etc. It supports a programming style similar to one would use in matlab and most matlab techniques have an analogue in numpy. SciPy builds on numpy and provides many different packages for optimization, root finding, statistics, linear algebra, interpolation, FFT and dsp tools, etc. Finally cvxopt is an optimization package which can solve linear and quadratic programming problems and also has a nice linear algebra interface. Now we will spend a bit more time on each of these packages.
Before we start let us point out http://www.scipy.org/NumPy_for_Matlab_Users, which has a comparison between matlab and numpy and gives numpy equivalents of matlab commands. If you’re not familiar with matlab, thats fine, even better, it means you won’t have any pre-conceived notions of how things should work. Also this http://www.scipy.org/Wiki/Documentation?action=AttachFile&do=get&target=scipy_tutorial.pdf is a very nice tutorial on SciPy and numpy which is more comprehensive than ours.