The Matrix library is a collection of object-oriented functions for
performing basic linear algebra tasks, such as matrix decomposition and
solutions to systems of linear equations, which are fundamental in
scientific, engineering, and statistical computations. The functions
are based on LAPACK, the Fortran standard for linear algebra for small
to medium-sized dense problems. The aim is to provide a consistent and
efficient set of S-Plus matrix operations and functions that reflect
intuitive notions from linear algebra as much as possible.

In the Matrix library, matrices are represented as objects of class
"Matrix".  There are also several subclasses, for example, "Hermitian",
"Orthogonal", and "LowerTriangular". These objects are similar to those
created by the S-PLUS function matrix(), but there some differences in
the creation and coercion functions, in subsetting and arithmetic
operations, and in the results of eigen(), qr(), and svd(). It should
not be assumed that objects of class "Matrix" can be used in every
S-PLUS function that accepts a matrix as input.

In addition to these changes, the Matrix library adds some new
capabilities to S-PLUS. There are functions for computing determinants,
matrix norms, and condition estimation, as well as the Schur, LU, and
symmetric-indefinite decompositions. Solve methods are available for
most decompositions, and overdetermined systems can now be handled.

A more detailed description can be found in the help files and the
S-PLUS Version 3.3 Supplement.