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" Toeplitz and circulant matrices : "
Robert M. Gray.
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BL
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| Record Number
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1025560
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b779930
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| Main Entry
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Gray, Robert M.,1943-
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| Title & Author
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Toeplitz and circulant matrices : : a review /\ Robert M. Gray.
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| Publication Statement
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Boston :: Now,, ©2006.
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| Series Statement
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Foundations and trends in communications and information theory ;; v. 2, issue 3
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| Page. NO
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1 online resource (ix, 93 pages) :: illustrations
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| ISBN
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1282823140
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: 1933019239
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: 1933019689
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: 9781282823143
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: 9781933019239
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: 9781933019680
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| Bibliographies/Indexes
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Includes bibliographical references.
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| Contents
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Cover13; -- Contents -- Introduction -- Toeplitz and Circulant Matrices -- Examples -- Goals and Prerequisites -- The Asymptotic Behavior of Matrices -- Eigenvalues -- Matrix Norms -- Asymptotically Equivalent Sequences of Matrices -- Asymptotically Absolutely Equal Distributions -- Circulant Matrices -- Eigenvalues and Eigenvectors -- Matrix Operations on Circulant Matrices -- Toeplitz Matrices -- Sequences of Toeplitz Matrices -- Bounds on Eigenvalues of Toeplitz Matrices -- Banded Toeplitz Matrices -- Wiener Class Toeplitz Matrices -- Matrix Operations on Toeplitz Matrices -- Inverses of Toeplitz Matrices -- Products of Toeplitz Matrices -- Toeplitz Determinants -- Applications to Stochastic Time Series -- Moving Average Processes -- Autoregressive Processes -- Factorization -- References.
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| Abstract
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Toeplitz and Circulant Matrices: A review derives in a tutorial manner the fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight in the hope of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject. By limiting the generality of the matrices considered, the essential ideas and results can be conveyed in a more intuitive manner without the mathematical machinery required for the most general cases. As an application the results are applied to the study of the covariance matrices and their factors of linear models of discrete time random processes. Toeplitz and Circulant Matrices: A review is written for students and practicing engineers in an accessible manner bringing this important topic to a wider audience.
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| Subject
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Toeplitz matrices.
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| Subject
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MATHEMATICS-- Matrices.
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| Subject
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Toeplitz matrices.
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| Dewey Classification
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512.9/434
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| LC Classification
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QA188.G714 2006eb
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