MATLAB is a computer program by MathWorks which allows one to easily manipulate matrices, plot functions and data, and implement algorithms in its own internal programming language. It runs on Windows, MacOS and Unix and is widely used in the teaching of linear algebra and numerical analysis. The language was invented by Cleve Moler in the late 1970s.
Free software alternatives to MATLAB include GNU Octave and Scilab, which have an identical (or at least very similar) syntax. Another free alternative is Python in combination with libraries like Numeric Python and SciPy.