MATLAB (MATrix LABoratory) is an interactive system for matrix-based computation designed for scientific and engineering use. It is good for many forms of numeric computation and visualization. Besides dealing with explicit matrices in linear algebra, it can handle differential equations, polynomials, signal processing, and other applications. Results can be made available both numerically and as excellent graphics.
Some classes at MIT require the use of MATLAB; it is also useful for many that don't. It may not be most suitable tool for your needs; e.g. Maple and Mathematica are better for symbolic math (MATLAB's symbolic math draws on part of Maple), Xess for spreadsheet work.
This document is intended partially as a MATLAB tutorial and partially as a reference.