Matrix Market Deli
Test matrices made to order ... while you wait
Note: Each generator is assembled into an application
using intercommunicating Frames, Java and Javascript. Consequently,
these generators can probably only be used with relatively recent browsers
(eg. Netscape or Internet Explorer versions 4 or above).
However most of the generators presented here are adapted from
Nicholas J. Higham's worthwhile
Test Matrix Toolbox .
Available Generators:
Clement
A tridiagaonal , square matrix with zero diagonal;
has explicitly known inverse, eigenvalues
and eigenvectors; may be symmetric ,
rank deficient .
Condition Estimate Counterexample
A set of ill conditioned matrices
which are counter examples to the LINPACK
condition number estimator.
Cyclic Column
A matrix with random cyclic columns;
For some values of parameters, it may be rank deficient .
DingDong
A symmetric , square, Hankel matrix
whose eigenvalues cluster around ±PI/2.
Dorr
A diagonally dominant , tridiagonal ,
M-matrix ,
possibly ill conditioned
for small values of the parameter.
Forsythe
A perturbed Jordan Block matrix.
Frank
An upper Hessenberg matrix
with ill conditioned
eigenvalues, whose determinant is 1.
Gear
A sinple defective ,
singular matrix with known
eigenvalues; can be rank deficient ,
and can have double and triple eigenvalues.
Hilbert
A symmetric , positive definite ,
totally positive , Hankel matrix;
a famous badly conditioned matrix; inverse is known explicitly.
Jordan
A Jordan Block , matrix;
it is defective with known eigenvalue.
Kahan
An upper trapezoidal matrix that has some
interesting properties regarding estimation of condition and rank.
Lauchli
A rectangular matrix; a well known example from least squares indicating
the dangers of A^{T} A.
Lotkin
An unsymmetric, ill conditioned ,
totally positive , and has many small, negative eigenvalues;
inverse has integer entries and is known explicitly.
Random
Random sparse matrices of arbitrary size and density.
Wilkinson
A matrix for which Gaussian elimination with partial pivoting yields
a large growth factor.

The Matrix Market is a service of the
Mathematical and Computational Sciences Division /
Information Technology Laboratory /
National Institute of Standards and Technology
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Page created 1997-03-03, last modified 2002-04-10.
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