Matrices

C

• GNU Scientific Library
• Meschach, matrix computations in C
• BLAS (Basic Linear Algebra Subprograms); Fortran and C code packaged in a library

C++

• Matrix Template Library (MTL)
• Scalar, Vector, Matrix and Tensor Library (SVMTL)
• Blitz++
  • For some interesting discussion of Template Metaprogramming, a basis for Blitz++, see this page of C++ Optimization Strategies and Techniques
• Cooperware Matrix (CwMtx)
• Matrix programs from Jean-Pierre Moreau
• See Numerican Recipes in C++

Java

• JAMA: A Java Matrix Package

Python

Lisp

Mathematica

Octave

Octave lives on matrices. I was able to create a 65536×65536 matrix, but I had to wait a minute or two:

a = rand(2^16,2^16)

Further Reading

• Linear Algebra entry from The Mathematical Altas
• Jim Hefferon has placed his GFDL/CC free text online