Additional functionality related to this tutorial has been introduced in subsequent versions of Mathematica. For the latest information, see Matrices and Linear Algebra.

Linear Algebra in Mathematica: References

Software References

ARPACK

ARPACK is a collection of Fortran77 subroutines designed to solve large-scale eigenvalue problems. http://www.caam.rice.edu/software/ARPACK

ATLAS

The ATLAS (Automatically Tuned Linear Algebra Software) project provides C and Fortran77 interfaces to a portable efficient BLAS implementation, as well as a few routines from LAPACK. http://math-atlas.sourceforge.net

HarwellBoeing

The HarwellBoeing matrix format is a popular storage and description format for sparse matrix data, described at http://math.nist.gov/MatrixMarket/formats.html. Many examples of matrices in this format can be found at http://math.nist.gov/MatrixMarket/index.html.

Matrix Market

The Matrix Market matrix format provides a simple mechanism to facilitate the exchange of sparse and dense matrix data, described at http://math.nist.gov/MatrixMarket/formats.html. Many examples of matrices in this format can be found at http://math.nist.gov/MatrixMarket/index.html.

METIS

METIS is a family of programs for partitioning unstructured graphs and hypergraphs and computing fill-reducing orderings of sparse matrices. http://www-users.cs.umn.edu/~karypis/metis/index.html

TAUCS

TAUCS is a library of sparse linear solvers. http://www.tau.ac.il/~stoledo/taucs

UMFPACK

UMFPACK is a set of routines for solving unsymmetric sparse linear systems, , using the Unsymmetric MultiFrontal method. http://www.cise.ufl.edu/research/sparse/umfpack

Other References

[1] Weisstein, E. W. MathWorld 2007. http://mathworld.wolfram.com

[2] Anderson, E., Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen. LAPACK Users' Guide, 3rd ed. Society for Industrial and Applied Mathematics, 1999.

[3] Golub, G. H. and C. F. van Loan. Matrix Computations, 3rd ed. The Johns Hopkins University Press, 1996.

[4] Meyer, C. D. Matrix Analysis and Applied Linear Algebra, 1st ed. The Society for Industrial and Applied Mathematics, 2000.