function A = lehmer(n)
%LEHMER Lehmer matrix.
%   A = GALLERY('LEHMER',N) is the symmetric positive definite 
%   N-by-N matrix such that A(i,j) = i/j for j >= i.
%
%   Properties:
%      A is totally nonnegative.  
%      INV(A) is tridiagonal and explicitly known.
%      N <= COND(A) <= 4*N*N.

%   References:
%   [1] M. Newman and J. Todd, "The evaluation of matrix inversion
%         programs", J. Soc. Indust. Appl Math, 6 (1958),pp. 466-476.
%   [2] Solutions to problem E710 (proposed by D.H. Lehmer): 
%         The inverse of a matrix, Amer. Math. Monthly, 53 (1946), 
%         pp. 534-535.
%   [3] J. Todd, Basic Numerical Mathematics, Vol. 2: Numerical 
%         Algebra, Birkhauser, Basel, and Academic Press, New York, 
%         1977, p. 154.
%
%   Copyright (c) 1984-98 by The MathWorks, Inc.
%   $Revision: 1.5 $  $Date: 1997/11/21 23:29:45 $

A = ones(n,1)*(1:n);
A = A./A';
A = tril(A) + tril(A,-1)';
