On some properties of positive definite toeplitz matrices and their possible applications

Abstract Various properties of a real symmetric Toeplitz matrix Σm with elements σjk= a|j−k|, 1 ⩽j,k⩽m, are reviewed here. Matrices of this kind often arise in applications in statistics, econometrics, psychometrics, structural engineering, multichannel filtering, reflection seismology, etc., and it is desirable to have techniques which exploit their special structure. Possible applications of the results related to their inverse, determinant, and eigenvalue problem are suggested.

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