//  J.C. Nash, Compact Numerical Methods for Computers: Linear
//  Algebra and Function Minimisation, second edition, Adam Hilger,
//  Bristol, 1990 (Appendix 1).
http://en.wikipedia.org/wiki/Toeplitz_matrix
http://en.wikipedia.org/wiki/Circulant_matrix
http://people.sc.fsu.edu/~burkardt/m_src/test_matrix/contents.m
http://orion.math.iastate.edu/burkardt/f_src/testmat/testmat.html
http://en.wikipedia.org/wiki/Hilbert_matrix
http://en.wikipedia.org/wiki/Hankel_matrix
http://www.mathworks.com/access/helpdesk/help/techdoc/index.html?/access/helpdesk/help/techdoc/ref/wilkinson.html&http://www.google.fr/search?q=matlab+wilkinson+matrix&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:fr:official&client=firefox-a
http://www.mathworks.com/access/helpdesk/help/techdoc/index.html?/access/helpdesk/help/techdoc/ref/wilkinson.html&http://www.google.fr/search?q=matlab+wilkinson+matrix&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:fr:official&client=firefox-a

Special Matrices

         Circulnt(col) returns the circulant matrix defined by the column col
Example: Circulnt({1,2,3,4})  [[1,4,3,2][2,1,4,3][3,2,1,4][4,3,2,1]]
Note: A circulant matrix is a special case of the Toeplitz matrix.

         Frank(n) returns the Frank matrix of order n
Example: Frank(4)  [[4,3,2,1][3,3,2,1][0,2,2,1][0,0,1,1]]

         Hadamard(n) returns a Hadamard matrix of order n
Needs: KProduct
Example: Hadamard(4)  [[1,1,1,1][1,-1,1,-1][1,1,-1,-1][1,-1,-1,1]]
Notes: Hadamard matrices exist only for n = 2 or n a multiple of 4. For an nn Hadamard matrix H, HTH = nI, where I is the identity matrix, and det(H) = nn/2. Hadamard matrices are used in various combinatorics problems such as the Reed-Muller error-correcting codes.

         Hankel(list) returns the corresponding Hankel matrix
Example: Hankel({1,1,1,6,21})  [[1,1,1][1,1,6][1,6,21]]
Note: Hankel matrices are symmetric.

         Hilbert(n) returns the Hilbert matrix of order n
Example: Hilbert(3)  [[1,1/2,1/3][1/2,1/3,1/4][1/3,1/4,1/5]]
Note: The inverse of a Hilbert matrix has integer elements. A Hilbert matrix is a special case of the Hankel matrix.

         IHilbert(n) returns the inverse of the order-n Hilbert matrix
Needs: Hilbert
Example: IHilbert(3)  [[9,-36,30][-36,192,-180][30,-180,180]]
Note: IHilbert(n) is usually faster than Hilbert(n)-1. For example, Hilbert(10)-1 takes about 17.2 seconds while IHilbert(10) takes about 4.0 seconds.

         Pascal(n) returns the Pascal matrix of order n
Example: Pascal(4)  [[1,1,1,1][1,2,3,4][1,3,6,10][1,4,10,20]]

         Toeplitz(row,col) returns the corresponding Toeplitz matrix
Needs: Reverse
Example: Toeplitz({a,b,c},{a,d,e})  [[a,b,c][d,a,b][e,d,a]]
Note: row[1] must equal col[1].

         Vanderm(list) returns the corresponding Vandermonde matrix
Example: Vanderm({v1,v2,v3})  [[1,1,1][v1,v2,v3][v12,v22,v32]]
Note: Vandermonde matrices appear in association with fitting polynomials to data. In particular, you can create a Vandermonde matrix from the x-values, augment the y-values to the bottom, perform an rref of the transpose, and obtain an interpolating polynomial by doing the sum xk-1mat[k,colDim(mat)], k=1, ?, rowDim(mat), where mat is the row-reduced matrix.


http://portal.acm.org/citation.cfm?id=14072
Varah, J. M. 1986. A generalization of the Frank matrix. SIAM J. Sci. Stat. Comput. 7, 3 (Jul. 1986), 835-839. DOI= http://dx.doi.org/10.1137/0907056

http://www.springerlink.com/content/n1u1538k1t274h85/
    Journal Title  - Numerische Mathematik
    Article Title  - Note on matrices with a very ill-conditioned eigenproblem
    Volume  - Volume 19
    Issue  - 2
    First Page  - 176
    Last Page  - 178
    Issue Cover Date  - 1972-04-21

    Author  - J. H. Wilkinson
    DOI  - 10.1007/BF01402528
    Link  - http://www.springerlink.com/content/n1u1538k1t274h85

http://www.mathworks.com/access/helpdesk/help/techdoc/index.html?/access/helpdesk/help/techdoc/ref/gallery.html&http://www.google.fr/search?q=matlab+test++matrix&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:fr:official&client=firefox-a

http://www.nmconsortium.org/FldRte/?id=76&page=Mathematical+Functions
Hadamard Matrix

Hankel Matrix

Hilbert Matrix

Identity Matrix

Inverse Hilbert Matrix

Magic Square

Matrix Of TRUE

Matrix Of FALSE

Matrix Of Ones

Matrix Of Zeros

Pascal Matrix

Peaks Matrix Generator

Prime Numbers

Rosser Matrix

Toeplitz Matrix

Vandermonde Matrix

Wilkinson Matrix

***************************************************

Largest Hilbert matrix computable :
-->tic;n= 202;A = testmatrix("hilb",n);cond(A),toc
 ans  =
    2.847+191
 ans  =
    0.056
-->tic;n= 202;A = testmatrix("hilb",n);toc
 ans  =
    0.001
-->n= 203;A = testmatrix("hilb",n);cond(A)
 !--error 264
Wrong value for argument 1: Must not contain NaN or Inf.

at line       8 of function cond called by :
n= 203;A = testmatrix("hilb",n);cond(A)


*********************************************************
-->tic;n= 202;A = makematrix_invhilbert(n);cond(A),toc
 ans  =

    3.811+190
 ans  =

    0.442
-->tic;n= 202;A = makematrix_invhilbert(n);toc
 ans  =

    3.811+190
 ans  =

    0.442
-->tic;n= 202;A = makematrix_invhilbert(n);toc
 ans  =

    0.387
*********************************************************
Matlab (Matlab script) :
>> tic;A = invhilb(202);cond(A),toc

ans =

  1.8896e+191

Elapsed time is 0.032036 seconds.
>> tic;A = invhilb(202);toc
Elapsed time is 0.001161 seconds.

*********************************************************
Scilab 4.1.2
-->tic;n= 202;A = makematrix_invhilbert(n);toc
 ans  =

    0.15
-->tic;n= 202;A = makematrix_invhilbert(n);cond(A),toc
 ans  =

    6.806+190
 ans  =

    0.213

