Cleve Moler is the creator of MATLAB. Moler was a numerical analyst specializing in matrix computation. Cleve Moler, the chairman of the computer-science department at the University of New Mexico, started developing MATLAB in the late 1970s. In the early 1970s, Moler participated in an effort organized by Argonne National Laboratory to produce a library of reliable, efficient FORTRAN subroutines for computing the eigenvalues of matrices (EISPACK) and solving systems of linear equations (LINPACK). In order to make these packages easier for students to use, Moler created MATLAB, whose name is a contraction of “Matrix Laboratory“. The original MATLAB was a FORTRAN program, designed for the era of time-sharing and ASCII terminals. It had only one data type (the matrix of complex doubles) and a fixed collection of 80 functions. Moler used the FORTRAN MATLAB in teaching numerical analysis at Stanford in 1979. Jack Little, an engineer, was exposed to it during a visit Moler made to Stanford University in 1983. Recognizing its commercial potential, he joined with Moler and Steve Bangert. Word of the program reached Jack Little, who grasped the potential of MATLAB in signal processing and control, and the possibility of making a successful software product based on MATLAB for the new IBM PC.

He designed it to give his students access to LINPACK and EISPACK without them having to learn FORTRAN.

Little and Steve Bangert developed PC MATLAB by porting Moler’s code from FORTRAN to C, adding user-defined functions (in effect making MATLAB into a programming language rather than a calculator), improved graphics, and libraries of MATLAB routines, the toolboxes. Moler, Little, and Bangert formed the Mathworks in 1984, with PC MATLAB as the first product. Their first sale was an order for ten copies placed by Professor Nick Trefethen at MIT.

Growth and Development

 MATLAB has indeed been a commercial success from the beginning, growing to more than 1,000,000 users and by 2006 to 1,200 Mathworkers, as the employees of Mathworks are known. MATLAB has, in effect, become the common language for the informal exchange of software and for algorithmic experiment in technical computing. The company remains privately held.

There have been several major revisions and enhancements to MATLAB, including an extended set of graphics tools and primitives, multidimensional arrays and lists (known in MATLAB as cell arrays), classes and objects, economical storage schemes and algorithms for sparse matrices, a debugger, a profiler, a GUI builder, a lower cost student edition, and Just-In-Time (JIT) compilation for improved performance. The computational core has been upgraded through the incorporation LAPACK (a state-of-the-art library for matrix computation), as well as software for computation of definite integrals, integration of ordinary differential equations, and root finders. 

The Mathworks logo is a picture (generated by MATLAB) of a numerical approximation to the fundamental mode of a vibrating L-shaped membrane, a topic that Moler discussed in his Stanford Ph.D. thesis in 1965.

Toolboxes created by the Mathworks and other contributors have expanded the scope of MATLAB, adding capabilities in areas such asoptimization, signal and image processing, fuzzy logic, splines, wavelets, statistics, partial differential equations, bioinformatics, and mathematical finance. SIMULINK, aeronautical ,  an extensible block diagram environment for simulation and model-based design appeared as a second Mathworks product in 1990.