Matlab vs Octave
Matlab, a proprietary system, is the premier language and toolkit for technical and analytical computing. GNU Octave is a truly free system that is largely compatible with, and approaches, Matlab's functionality. Matlab installations typically cost several hundred to several thousand US dollars per user, depending on selected toolboxes. Octave is free.
Both systems support processing of multidimensional numeric data with a wide variety of mathematical operations. Both also provide sophisticated graphing capabilities. Both are programmable by means of a nearly identical scripting language (files typically have the .m extension). Octave, however, allows for slightly tighter integration on POSIX systems due to allowing a # to indicate comments.
While both use a command line as the primary interface, Matlab ships with a powerful Integrated Development Environment (IDE). Octave does not ship with an IDE.