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The Clement or Sylvester-Kac matrix is a tridiagonal matrix with zerodiagonal and simple integer entries. Its spectrum is known explicitly andconsists of integers which makes it a useful test matrix for numericaleigenvalue computations. We consider a new class of appealing two-parameterextensions of this matrix which have the same simple structure and whoseeigenvalues are also given explicitly by a simple closed form expression. Theaim of this paper is to present in an accessible form these new matrices andexamine some numerical results regarding the use of these extensions as testmatrices for numerical eigenvalue computations.

Tridiagonal test matrices for eigenvalue computations: two-parameter extensions of the Clement matrix