Higham's Test Matrices

TEST_MATRIX is a MATLAB library which defines a set of test 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 of the matrices come from a MATLAB M file collection developed by Nicholas Higham, Department of Mathematics, University of Manchester, and maintained in the "testmatrix" file somewhere at the MATLAB web site.

An earlier version of the collection is available, again as MATLAB M files, in ACM TOMS Algorithm 694, in the TOMS directory of the NETLIB web site.


TEST_MATRIX is available in a MATLAB version.

Related Data and Programs:

LINPACK, a MATLAB library which provides some linear algebra operations for certain standard storage formats.

LINPLUS, a MATLAB library which provides some simple linear algebra operations for a number of storage formats.

TEST_MAT, a MATLAB library which defines a number of test matrices.


  1. TS Chow,
    A class of Hessenberg matrices with known eigenvalues and inverses,
    SIAM Review,
    Volume 11, Number 3, July 1969, pages 391-395.
  2. Robert Gregory, David Karney,
    A Collection of Matrices for Testing Computational Algorithms,
    Wiley, 1969,
    ISBN: 0882756494,
    LC: QA263 G862.
  3. Nicholas Higham,
    Algorithm 694: A Collection of Test Matrices in MATLAB,
    ACM Transactions on Mathematical Software,
    Volume 17, Number 3, September 1991, pages 289-305.
  4. Morris Newman, John Todd,
    The evaluation of matrix inversion programs,
    Journal of the Society for Industrial and Applied Mathematics,
    Volume 6, Number 4, 1958, pages 466-476.
  5. Andrew Wathen,
    Realistic eigenvalue bounds for the Galerkin mass matrix,
    IMA Journal of Numerical Analysis,
    Volume 7, 1987, pages 449-457.
  6. Joan Westlake,
    A Handbook of Numerical Matrix Inversion and Solution of Linear Equations,
    John Wiley, 1968.
  7. James Wilkinson,
    Rounding Errors in Algebraic Processes,
    Prentice Hall, 1963,
    ISBN: 0-486-67999-3.
  8. James Wilkinson,
    The Algebraic Eigenvalue Problem,
    Oxford University Press, 1988,
    ISBN: 0198534183.
  9. James Wilkinson, Christian Reinsch,
    Handbook for Automatic Computation,
    Volume II, Linear Algebra, Part 2,
    Springer, 1971,
    ISBN: 0387054146.

Source Code:

Examples and Tests:

You can go up one level to the MATLAB source codes.

Last revised on 01 September 2005.