www.gusucode.com > elmat工具箱matlab源码程序 > elmat/private/invol.m
function A = invol(n,classname) %INVOL Involutory matrix. % A = GALLERY('INVOL',N) is an N-by-N involutory (A*A = EYE(N)) % and ill-conditioned matrix. It is a diagonally scaled version % of HILB(N). % % Note: B = (EYE(N)-A)/2 and B = (EYE(N)+A)/2 are % idempotent (B*B = B). % Reference: % A. S. Householder and J. A. Carpenter, The singular values % of involutory and of idempotent matrices, % Numer. Math. 5 (1963), pp. 234-237. % % Copyright 1984-2005 The MathWorks, Inc. A = hilb(n,classname); d = -n; A(:, 1) = d*A(:, 1); for i = 1:n-1 d = -(n+i)*(n-i)*d/(i*i); A(i+1, :) = d*A(i+1, :); end