Publisher DOI: 10.1016/j.laa.2014.07.023
Title: Inverses, determinants, eigenvalues, and eigenvectors of real symmetric Toeplitz matrices with linearly increasing entries
Language: English
Authors: Bünger, Florian 
Keywords: Determinant;Eigenvalue;Eigenvector;Inverse;Toeplitz matrix
Issue Date: 7-Aug-2014
Publisher: American Elsevier Publ.
Source: Linear Algebra and Its Applications (459): 595-619 (2014-10-15)
Journal or Series Name: Linear algebra and its applications 
Abstract (english): We explicitly determine the skew-symmetric eigenvectors and corresponding eigenvalues of the real symmetric Toeplitz matricesT=T(a,b,n):=( a+b|j-k|)1≤j,k≤n of order n≥3 where a, b ∈ ℝ, b ≠0. The matrix T is singular if and only if c := a/b = -n-1/2. In this case we also explicitly determine the symmetric eigenvectors and corresponding eigenvalues of T. If T is regular, we explicitly compute the inverse T- 1, the determinant det T, and the symmetric eigenvectors and corresponding eigenvalues of T are described in terms of the roots of the real self-inversive polynomial pn(δ;z):=(zn+1- δzn-δz+1)/(z+1) if n is even, and pn(δ; z):=zn+1-δzn-δz+1 if n is odd, δ:=1+2/(2c+n-1). © 2014 Elsevier Inc.
ISSN: 0024-3795
Institute: Zuverlässiges Rechnen E-19 
Type: (wissenschaftlicher) Artikel
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