Toeplitz and Circulant Matrices: A review (Foundations and Trends in Communications and Information The)
Robert M. Gray | 2006-01-02 00:00:00 | Now Publishers Inc | 104 | Information Theory
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.
Reviews
This is an excellent review article published in the top journal Foundations and Trends in Communications and Information Theory. This journal only publishes one article once and also publishes as a book version.
Reviews
The 'book' gives no insight into anything. A better title for the book is: An incomplete proof of Szego's theorem with some vague references to its application.
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