MATCALC is an easy-to-use interactive matrix calculation package designed
for:
   easy solution of linear algebra and matrix problems involving
   either real or complex numbers,
   easy solution of systems of linear equations,
   teaching fundamental vector space and linear transformation ideas 
        at university undergraduate level,
   teaching modern computational methods of linear and matrix algebra,
   polynomial arithmetic,
   solution of matrix-related problems such as finding 
   zeroes of real or complex polynomials, 
   linear least-squares fits of multivariable models, etc.

Basic commands are included for entering matrices, matrix arithmetic, 
adjoining matrices, selecting matrix elements, selecting rows or columns, 
and for creating special matrices.
 
Predefined functions and procedures are included for such problems as
polynomial arithmetic, solving systems of linear equations, finding
triangular factorizations, analysing row-echelon matrices,
finding eigenvalues and eigenvectors, obtaining Jordan forms, and for
obtaining singular-value decompositions.
 
MATCALC includes full programming capabilities with facilities for logical
relations and conditions, IF and LOOP blocks and user-defined functions
and procedures.
 
Users can also create their own configurations of MATCALC tailored to meet
their specific requirements. They can easily create subsets of MATCALC by
omitting selected predefined functions and procedures.  They can also write
their own functions and procedures in C and add them to MATCALC.

The minimal configuration of MATCALC can be used as a desk calculator for
matrix arithmetic or complex arithmetic. In this configuration it is
suitable for users with a high school background in mathematics.  In its
full configuration the package has been used to do original research in
mathematics, engineering and psychology.  The minimum computing knowledge
required to use  MATCALC is a knowledge of how to log on and off a computer.
 
MATCALC has been designed to bridge the gap which seems to exist between
the methods currently taught in many linear algebra courses in Mathematics
Departments and the modern computational methods used in standard software
packages such as LINPACK and EISPACK.  One reason for this gap is that the
standard routines of LINPACK and EISPACK are designed for fast computation
on non-singular systems, whereas many of the central problems of linear
algebra courses lead immediately to  singular problems.

For example, fundamental vector space ideas such as span, linear
dependence or independence, construction of a basis, dimension of a space
or subspace etc. frequently lead to singular problems.

A similar comment is applicable to eigenvalue and eigenvector problems. 
One of the important topics in most linear algebra courses is that of
finding the Jordan form of a matrix. In software packages the possible
existence of Jordan forms is ignored, presumably because the unavoidable
rounding errors mean that a Jordan form ``never'' occurs.
 
MATCALC recognizes the fact that triangular factorizations (such as the
LU factorization and the QR factorization) are central to all modern
computational methods.  However, these factorizations have been specially
adapted to handle singular matrices.  Thus, the LU factorization of
MATCALC produces a factorization into a lower triangular matrix and a
row-echelon matrix,  rather than the LINPACK factorization into lower and
upper triangular matrices. The QR factorization has been similarly modified
in MATCALC. Commands have been included to facilitate the analysis of these
row-echelon matrices.