# 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 ATA.
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. [ ]