--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/toolbox/clement.m	Thu May 07 18:36:24 2015 +0200
@@ -0,0 +1,38 @@
+function A = clement(n, k)
+%CLEMENT   Clement matrix - tridiagonal with zero diagonal entries.
+%          CLEMENT(N, K) is a tridiagonal matrix with zero diagonal entries
+%          and known eigenvalues.  It is singular if N is odd.  About 64
+%          percent of the entries of the inverse are zero.  The eigenvalues
+%          are plus and minus the numbers N-1, N-3, N-5, ..., (1 or 0).
+%          For K = 0 (the default) the matrix is unsymmetric, while for
+%          K = 1 it is symmetric.
+%          CLEMENT(N, 1) is diagonally similar to CLEMENT(N).
+
+%          Similar properties hold for TRIDIAG(X,Y,Z) where Y = ZEROS(N,1).
+%          The eigenvalues still come in plus/minus pairs but they are not
+%          known explicitly.
+%
+%          References:
+%          P.A. Clement, A class of triple-diagonal matrices for test
+%             purposes, SIAM Review, 1 (1959), pp. 50-52.
+%          A. Edelman and E. Kostlan, The road from Kac's matrix to Kac's
+%             random polynomials. In John~G. Lewis, editor, Proceedings of
+%             the Fifth SIAM Conference on Applied Linear Algebra Society
+%             for Industrial and Applied Mathematics, Philadelphia, 1994,
+%             pp. 503-507.
+%          O. Taussky and J. Todd, Another look at a matrix of Mark Kac,
+%             Linear Algebra and Appl., 150 (1991), pp. 341-360.
+
+if nargin == 1, k = 0; end
+
+n = n-1;
+
+x = n:-1:1;
+z = 1:n;
+
+if k == 0
+   A = diag(x, -1) + diag(z, 1);
+else
+   y = sqrt(x.*z);
+   A = diag(y, -1) + diag(y, 1);
+end