Toeplitz and Circulant Matrices : A Review (Foundations and Trends® in Communications and Information Theory)

Gray, Robert M.

now publishers Inc（2006/01発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 100 p.
• 言語 ENG
• 商品コード 9781933019239
• DDC分類 512.9434

Full Description

Toeplitz and Circulant Matrices 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. The book has been written for students and practicing engineers in an accessible manner bringing this important topic to a wider audience.

Contents

1. Introduction 2. The Asymptotic Behavior of Matrices 3. Circulant Matrices 4. Toeplitz Matrices 5. Matrix Operations on Toeplitz Matrices 6. Applications to Stochastic Time Series