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- W2962815727 abstract "When 0<ρ<1, the Kac–Murdock–Szegö matrix Kn(ρ)=[ρ|j−k|]j,k=1n is a Toeplitz correlation matrix with many applications and very well known spectral properties. We study the eigenvalues and eigenvectors of Kn(ρ) for the general case where ρ is complex, pointing out similarities and differences to the case 0<ρ<1. We then specialize our results to real ρ with ρ>1, emphasizing the continuity of the eigenvalues as functions of ρ. For ρ>1, we develop simple approximate formulas for the eigenvalues and pinpoint all eigenvalues' locations. Our study starts from a certain polynomial whose zeros are connected to the eigenvalues by elementary formulas. We discuss relations of our results to earlier results of W.F. Trench." @default.
- W2962815727 created "2019-07-30" @default.
- W2962815727 creator A5062242606 @default.
- W2962815727 date "2018-09-01" @default.
- W2962815727 modified "2023-10-18" @default.
- W2962815727 title "Spectral properties of Kac–Murdock–Szegö matrices with a complex parameter" @default.
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- W2962815727 doi "https://doi.org/10.1016/j.laa.2018.05.004" @default.
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