**test_matrix**,
a C code which
defines test matrices for which the condition number, determinant,
eigenvalues, eigenvectors, inverse, null vectors, P*L*U factorization
or linear system solution are known. Examples include the
Fibonacci, Hilbert, Redheffer, Vandermonde, Wathen and Wilkinson
matrices.

A wide range of matrix dimensions, forms and properties are available. These matrices may be useful in testing an algorithm for correctness on a variety of problems.

Many of the matrices can be rectangular, with the user specifying the number of rows and columns. Almost all the matrices can be made of arbitrary size, with the user specifying the dimension.

Many different matrix zero structures are available, including diagonal, bidiagonal, tridiagonal, pentadiagonal, banded, upper and lower triangular, and Hessenberg.

Many different matrix symmetry patterns are available, including symmetric, antisymmetric, persymmetric, circulant, Toeplitz, and Hankel.

Matrices are available with known inverses, condition numbers, determinants, rank, eigenvalues, and characteristic polynomials. Other matrix properties include positive definiteness, positivity, zero/one, and adjacency matrices.

Many of the matrices come from a MATLAB M file collection developed by Nicholas Higham, Department of Mathematics, University of Manchester.

An earlier version of the collection is available in ACM TOMS Algorithm 694, in the TOMS directory of the NETLIB web site.

Many of these matrices, and many other matrices, are available at https://math.nist.gov, the Matrix Market web site.

The information on this web page is distributed under the MIT license.

**test_matrix** is available in
a C version and
a C++ version and
a Fortran77 version and
a Fortran90 version and
a MATLAB version and
an Octave version and
a Python version.

clapack_test, a C code which illustrates the use of the CLAPACK library, a translation of the Fortran77 BLAS and LAPACK linear algebra libraries, including single and double precision, real and complex arithmetic.

jacobi_eigenvalue, a C code which implements the Jacobi iteration for the iterative determination of the eigenvalues and eigenvectors of a real symmetric matrix.

levenshtein_matrix, a C code which returns the Levenshtein distance matrix defined by two strings.

polynomial_conversion, a C code which converts representations of a polynomial between monomial, Bernstein, Chebyshev, Hermite, Lagrange, Laguerre and other forms.

wathen_matrix, a C code which compares storage schemes (full, banded, sparse triplet) and solution strategies (Linpack full, Linpack banded, conjugate gradient (CG)) for linear systems involving the Wathen matrix, which can arise when solving a problem using the finite element method (FEM).

- test_matrix.c, the source code.
- test_matrix.sh, compiles the source code.
- test_matrix.h, the include file.