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) | 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). |
URI: | http://hdl.handle.net/11420/7882 | ISSN: | 0024-3795 | Journal: | Institute: | Zuverlässiges Rechnen E-19 | Document Type: | Article |
Appears in Collections: | Publications without fulltext |
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