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Inverses , determinants , eigenvalues , and eigenvectors of real symmetric Toeplitz matrices with linearly increasing entries
| Content Provider | Semantic Scholar |
|---|---|
| Author | Bünger, Florian |
| Copyright Year | 2014 |
| Abstract | We explicitly determine the skew-symmetric eigenvectors and corresponding eigenvalues of the real symmetric Toeplitz matrices T = T (a, b, n) := (a+ b|j − k|)1≤j,k≤n of order n ≥ 3 where a, b ∈ R, b 6= 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 detT , 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) := (z −δz−δz+1)/(z+1) if n is even, and pn(δ; z) := z −δz−δz+1 if n is odd, δ := 1+2/(2c+n−1). |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.ti3.tu-harburg.de/buenger/publications/toeplitz_spectra_2014.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Plant Roots Polynomial Singular The Matrix Toeplitz Hash Algorithm |
| Content Type | Text |
| Resource Type | Article |
