EXPLICIT EIGENVALUES AND INVERSES OF TRIDIAGONAL TOEPLITZ MATRICES WITH FOUR PERTURBED CORNERS
نویسندگان
چکیده
منابع مشابه
Characterizing the inverses of block tridiagonal, block Toeplitz matrices
We consider the inversion of block tridiagonal, block Toeplitz matrices and comment on the behaviour of these inverses as one moves away from the diagonal. Using matrix Möbius transformations, we first present an O(1) representation (with respect to the number of block rows and block columns) for the inverse matrix and subsequently use this representation to characterize the inverse matrix. The...
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We generalize some recent results on the spectra of tridiagonal matrices, providing explicit expressions for the characteristic polynomial of some perturbed tridiagonal k-Toeplitz matrices. The calculation of the eigenvalues (and associated eigenvectors) follows straightforward. Mathematics Subject Classification: 15A18, 42C05, 33C45
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The eigenvalues of a nonhermitian Toeplitz matrix A are usually highly sensitive to perturbations, having condition numbers that increase exponentially with the dimension N. An equivalent statement is that the resolvent ( ZZ A)’ of a Toeplitz matrix may be much larger in norm than the eigenvalues alone would suggest-exponentially large as a function of N, even when z is far from the spectrum. B...
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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 explic...
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Article history: Received 27 April 2009 Accepted 13 April 2010 Available online 15 May 2010 Submitted by C. Mehl AMS classification: 15A09 39A10 65F99
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ژورنال
عنوان ژورنال: The ANZIAM Journal
سال: 2008
ISSN: 1446-1811,1446-8735
DOI: 10.1017/s1446181108000102