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Interlacement of the even and odd spectra of real symmetric Toeplitz matrices

It is shown that for every n the even and odd spectra of real symmetric Toeplitz matrices Tn=(tr−s)nr,s=1 are interlaced if tr = 1π∫π0⨍(θ)cos rθ dθ, r=0,1,2,…, where f is monotonic and nonconstant.

William F. Trench | W. F. Trench

[1] Shmuel Friedland. Inverse Eigenvalue Problems for Symmetric Toeplitz Matrices , 1992, SIAM J. Matrix Anal. Appl..

[2] F. Grünbaum. Toeplitz matrices commuting with tridiagonal matrices , 1981 .

[3] F. Grünbaum. Eigenvectors of a Toeplitz Matrix: Discrete Version of the Prolate Spheroidal Wave Functions , 1981 .

[4] William F. Trench,et al. Numerical solution of the eigenvalue problem for symmetric rationally generated Toeplitz matrices , 1988 .

[5] H. J. Landau,et al. The inverse eigenvalue problem for real symmetric Toeplitz matrices , 1994 .

[6] Alan L. Andrew,et al. Eigenvectors of certain matrices , 1973 .

[7] G. Szegő,et al. On the Eigen-Values of Certain Hermitian Forms , 1953 .

[8] A. Cantoni,et al. Eigenvalues and eigenvectors of symmetric centrosymmetric matrices , 1976 .

[9] U. Grenander,et al. Toeplitz Forms And Their Applications , 1958 .

[10] Y. Genin,et al. Spectral properties of finite Toeplitz matrices , 1984 .

[11] William F. Trench,et al. On the eigenvalue problem for Toeplitz band matrices , 1985 .

[12] Dirk P. Laurie. A numerical approach to the inverse Toeplitz Eigenproblem , 1988 .

[13] D. Slepian. Prolate spheroidal wave functions, fourier analysis, and uncertainty — V: the discrete case , 1978, The Bell System Technical Journal.