The interesting spectral interlacing property for a certain tridiagonal matrix

Abstract

In this paper, a new tridiagonal matrix, whose eigenvalues are the same as the Sylvester-Kac matrix of the same order, is provided. The interest of this matrix relies also in that the spectrum of a principal submatrix is also of a Sylvester-Kac matrix given rise to an interesting spectral interlacing property. It is proved alternatively that the initial matrix is similar to the Sylvester-Kac matrix.

The spectrum of a new class of Sylvester-Kac matrices

“…, n. Since then, many extensions and proofs have been proposed. Perhaps the most pertinent results can be found in [2][3][4][7][8][9][10][11][12][13][14] and references therein. The matrix A n , which we call Sylvester-Kac matrix, became also known as Clement matrix due to the independent study of P.A.…”