MATLAB (an abbreviation of "MATrix LABoratory"[18]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.

An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamic and embedded systems.

[21] Moler became a math professor at the University of New Mexico and started developing MATLAB for his students[21] as a hobby.

[22] He developed MATLAB's initial linear algebra programming in 1967 with his one-time thesis advisor, George Forsythe.

[21] The software was disclosed to the public for the first time in February 1979 at the Naval Postgraduate School in California.

They decided to reprogram MATLAB in C and market it for the IBM desktops that were replacing mainframe computers at the time.

[22] MATLAB was first released as a commercial product in 1984 at the Automatic Control Conference in Las Vegas.

[21][22] MathWorks, Inc. was founded to develop the software[26] and the MATLAB programming language was released.

[24] The first MATLAB sale was the following year, when Nick Trefethen from the Massachusetts Institute of Technology bought ten copies.

[22] The software was popularized largely thanks to toolboxes created by experts in various fields for performing specialized mathematical tasks.

[25] Many of the toolboxes were developed as a result of Stanford students that used MATLAB in academia, then brought the software with them to the private sector.

[22] Over time, MATLAB was re-written for early operating systems created by Digital Equipment Corporation, VAX, Sun Microsystems, and for Unix PCs.

[24] In 2000, MathWorks added a Fortran-based library for linear algebra in MATLAB 6, replacing the software's original LINPACK and EISPACK subroutines that were in C.[24] MATLAB's Parallel Computing Toolbox was released at the 2004 Supercomputing Conference and support for graphics processing units (GPUs) was added to it in 2010.

Valid function names begin with an alphabetic character, and can contain letters, numbers, or underscores.

An example of a simple class is provided below: When put into a file named hello.m, this can be executed with the following commands: MATLAB has tightly integrated graph-plotting features.

[49] A wrapper function is created allowing MATLAB data types to be passed and returned.

[59] As alternatives to the MuPAD based Symbolic Math Toolbox available from MathWorks, MATLAB can be connected to Maple or Mathematica.