Description 
1 online resource 
Summary 
Circulant matrices have been around for a long time and have been extensively used in many scientific areas. This book studies the properties of the eigenvalues for various types of circulant matrices, such as the usual circulant, the reverse circulant, and the kcirculant when the dimension of the matrices grow and the entries are random. In particular, the behavior of the spectral distribution, of the spectral radius and of the appropriate point processes are developed systematically using the method of moments and the various powerful normal approximation results. This behavior varies according as the entries are independent, are from a linear process, and are light or heavytailed. Arup Bose obtained his B. Stat., M. Stat. and Ph. D. degrees from the Indian Statistical Institute. He has been on its faculty at the Theoretical Statistics and Mathematics Unit, Kolkata, India since 1991. He is a Fellow of the Institute of Mathematical Statistics, and of all three national science academies of India. He is a recipient of the S.S. Bhatnagar Prize and the C.R. Rao Award. He is the author of three books: Patterned Random Matrices, Large Covariance and Autocovariance Matrices (with Monika Bhattacharjee) and UStatistics, M_mEstimators and Resampling (with Snigdhansu Chatterjee). Koushik Saha obtained a B. Sc. in Mathematics from Ramakrishna Mission Vidyamandiara, Belur and an M. Sc. in Mathematics from Indian Institute of Technology Bombay. He obtained his Ph. D. degree from the Indian Statistical Institute under the supervision of Arup Bose. His thesis on circulant matrices received high praise from the reviewers. He has been on the faculty of the Department of Mathematics, Indian Institute of Technology Bombay since 2014 
Bibliography 
Includes bibliographical references and index 
Notes 
Arup Bose obtained his B. Stat., M. Stat. and Ph. D. degrees from the Indian Statistical Institute. He has been on its faculty at the Theoretical Statistics and Mathematics Unit, Kolkata, India since 1991. He is a Fellow of the Institute of Mathematical Statistics, and of all three national science academies of India. He is a recipient of the S.S. Bhatnagar Prize and the C.R. Rao Award. He is the author of three books: Patterned Random Matrices, Large Covariance and Autocovariance Matrices (with Monika Bhattacharjee) and UStatistics, M_mEstimators and Resampling (with Snigdhansu Chatterjee). Koushik Saha obtained a B. Sc. in Mathematics from Ramakrishna Mission Vidyamandiara, Belur and an M. Sc. in Mathematics from Indian Institute of Technology Bombay. He obtained his Ph. D. degree from the Indian Statistical Institute under the supervision of Arup Bose. His thesis on circulant matrices received high praise from the reviewers. He has been on the faculty of the Department of Mathematics, Indian Institute of Technology Bombay since 2014 

Print version record 
Subject 
Eigenvalues  Problems, exercises, etc


Matrices  Problems, exercises, etc


Random matrices  Problems, exercises, etc


Eigenvalues.


MATHEMATICS  Algebra  Intermediate.


MATHEMATICS  Probability & Statistics  Bayesian Analysis.


Matrices.


Random matrices.

Genre/Form 
Problems and exercises.

Form 
Electronic book

Author 
Saha, Koushik, author.

ISBN 
0429435509 

0429788177 

0429788185 

0429788193 

9780429435508 

9780429788178 

9780429788185 

9780429788192 
