Matrix Market Deli

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^TA.

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.