Environment

• interactive — type matrix expressions and see results
• development — full development environment for developing programs and commands
• automatically compiled code

General features and matrix operators

• support for real and complex values
• joining by rows or columns
• addition, subtraction, multiplication, scalar division
• elementwise arithmetic
• transposition and reshaping
• Kronecker and Hadamard products
• inner and outer products

• Code the function, function and gradient, or function, gradient, and Hessian
• Newton–Raphson, BFGS, DFP, BHHH, Nelder–Mead, and Gauss–Newton techniques
• Versions for general problems and statistical problems like maximum likelihood
  
• Debugger
• Covariance matrix based on Hessian, outer product of gradients, or robust/sandwich
  

Mathematical and matrix functions

• LAPACK numerical analysis routines
• Hundreds of mathematical, string, and matrix utility functions**
  
• symmetric, nonsymmetric, and generalized inverses
• Cholesky, LU, QR, and SVD solvers
• transcendental and trigonometric functions
• gamma and factorial functions
• density and distribution functions
• polynomial evaluation, arithmetic, and calculus
• Hilbert, Toeplitz, and Vandermonde matrices
• Duplication, commutation, and elimination matrices
  
• random-number generation
• fast Fourier analysis
• cubic splines
• means, sums, minimums, and maximums of matrices
• Numerical first and second derivatives
  

Object-oriented programming

• Inheritance
• Virtual functions
  
• Encapsulation of data structures and programs
  

Decompositions

• eigenvalues and eigenvectors
• Cholesky
• LU and LUD
• QR
• Schur
• Hessenberg
  
• singular value
• permutation matrices

Data accumulation

• cross products
• cross products of deviations from means
• weighted and GLS-type cross products
• support for quad-precision cross products

Stata interface

• convert Stata datasets to matrices and vice versa
• virtual matrix views onto dataset
• access and set estimation-class and other macros
• manipulate dataset value labels

Other features

• string scalars and matrices
• file I/O, including buffered I/O
• C-like syntax
• fast execution