The `Clement' matrix is a tridiagonal matrix with zero diagonal entries and known eigenvalues. The symmetric case is diagonally similar to the unsymmetric case.

If the order is odd, the matrix is singular, otherwise the inverse is known and may be computed here.


A test case for computations of matrix inverses and eigenvalues. The eigenvalues are ±(N-1), ±(N-3), ±(N-5), ..., (±1 or 0). About 64% of the entries of the inverse (for even order) are zero.


  1. This generator is adapted from Nicholas J. Higham's Test Matrix Toolbox.
  2. P.A. Clement, A class of triple-diagonal matrices for test purposes, SIAM Review, 1 (1959), pp. 50-52.
  3. 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.
  4. O. Taussky and J. Todd, Another look at a matrix of Mark Kac, Linear Algebra and Appl., 150 (1991), pp. 341-360.

The Matrix Market is a service of the Mathematical and Computational Sciences Division / Information Technology Laboratory / National Institute of Standards and Technology

[ MatrixMarket Home ] [ MatrixMarket Deli Home ] [ Search ] [ Browse ] [ Resources ]

Page created 1997-03-03, last modified 2000-08-06. [ ]