>> help gallery
GALLERY Higham test matrices.
    [out1,out2,...] = GALLERY(matname, param1, param2, ...)
    takes matname, a string that is the name of a matrix family, and
    the family's input parameters. See the listing below for available
    matrix families. Most of the functions take an input argument
    that specifies the order of the matrix, and unless otherwise
    stated, return a single output.
    For additional information, type "help private/matname", where matname
    is the name of the matrix family.

    cauchy    Cauchy matrix.
    chebspec  Chebyshev spectral differentiation matrix.
    chebvand  Vandermonde-like matrix for the Chebyshev polynomials.
    chow      Chow matrix -- a singular Toeplitz lower Hessenberg matrix.
    circul    Circulant matrix.
    clement   Clement matrix -- tridiagonal with zero diagonal entries.
    compar    Comparison matrices.
    condex    Counter-examples to matrix condition number estimators.
    cycol     Matrix whose columns repeat cyclically.
    dorr      Dorr matrix -- diagonally dominant, ill-conditioned, tridiagonal.
              (One or three output arguments, sparse)
    dramadah  Matrix of ones and zeroes whose inverse has large integer entries.
    fiedler   Fiedler matrix -- symmetric.
    forsythe  Forsythe matrix -- a perturbed Jordan block.
    frank     Frank matrix -- ill-conditioned eigenvalues.
    gearmat   Gear matrix.
    grcar     Grcar matrix -- a Toeplitz matrix with sensitive eigenvalues.
    hanowa    Matrix whose eigenvalues lie on a vertical line in the complex
              plane.
    house     Householder matrix. (Three output arguments)
    invhess   Inverse of an upper Hessenberg matrix.
    invol     Involutory matrix.
    ipjfact   Hankel matrix with factorial elements. (Two output arguments)
    jordbloc  Jordan block matrix.
    kahan     Kahan matrix -- upper trapezoidal.
    kms       Kac-Murdock-Szego Toeplitz matrix.
    krylov    Krylov matrix.
    lauchli   Lauchli matrix -- rectangular.
    lehmer    Lehmer matrix -- symmetric positive definite.
    leslie    Leslie matrix.
    lesp      Tridiagonal matrix with real, sensitive eigenvalues.
    lotkin    Lotkin matrix.
    minij     Symmetric positive definite matrix MIN(i,j).
    moler     Moler matrix -- symmetric positive definite.
    neumann   Singular matrix from the discrete Neumann problem (sparse).
    orthog    Orthogonal and nearly orthogonal matrices.
    parter    Parter matrix -- a Toeplitz matrix with singular values near PI.
    pei       Pei matrix.
    poisson   Block tridiagonal matrix from Poisson's equation (sparse).
    prolate   Prolate matrix -- symmetric, ill-conditioned Toeplitz matrix.
    randcolu  Random matrix with normalized cols and specified singular values.
    randcorr  Random correlation matrix with specified eigenvalues.
    randhess  Random, orthogonal upper Hessenberg matrix.
    randjorth Random J-orthogonal matrix.
    rando     Random matrix with elements -1, 0 or 1.
    randsvd   Random matrix with pre-assigned singular values and specified
              bandwidth.
    redheff   Matrix of 0s and 1s of Redheffer.
    riemann   Matrix associated with the Riemann hypothesis.
    ris       Ris matrix -- a symmetric Hankel matrix.
    smoke     Smoke matrix -- complex, with a "smoke ring" pseudospectrum.
    toeppd    Symmetric positive definite Toeplitz matrix.
    toeppen   Pentadiagonal Toeplitz matrix (sparse).
    tridiag   Tridiagonal matrix (sparse).
    triw      Upper triangular matrix discussed by Wilkinson and others.
    wathen    Wathen matrix -- a finite element matrix (sparse, random entries).
    wilk      Various specific matrices devised/discussed by Wilkinson.
              (Two output arguments)

    GALLERY(3) is a badly conditioned 3-by-3 matrix.
    GALLERY(5) is an interesting eigenvalue problem.  Try to find
    its EXACT eigenvalues and eigenvectors.