Matrix Analysis and Entrywise Positivity Preservers

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Matrix Analysis and Entrywise Positivity Preservers

Regular price $96.39
Condition - New
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Regular price $96.39
Condition - New
2 In stock

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Summary

This is the first book on matrix and kernel transforms preserving positivity structures. It is self-contained and only requires modest prerequisites in analysis and linear algebra. Covering deep results and modern progress, the book succeeds as an introduction for beginners and a comprehensive reference for experts.

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Matrix Analysis and Entrywise Positivity Preservers by Apoorva Khare

Matrices and kernels with positivity structures, and the question of entrywise functions preserving them, have been studied throughout the 20th century, attracting recent interest in connection to high-dimensional covariance estimation. This is the first book to systematically develop the theoretical foundations of the entrywise calculus, focusing on entrywise operations - or transforms - of matrices and kernels with additional structure, which preserve positive semidefiniteness. Designed as an introduction for students, it presents an in-depth and comprehensive view of the subject, from early results to recent progress. Topics include: structural results about, and classifying the preservers of positive semidefiniteness and other Loewner properties (monotonicity, convexity, super-additivity); historical connections to metric geometry; classical connections to moment problems; and recent connections to combinatorics and Schur polynomials. Based on the author's course, the book is structured for use as lecture notes, including exercises for students, yet can also function as a comprehensive reference text for experts.
'Positive definite matrices, kernels, sequences and functions, and operations on them that preserve their positivity, have been studied intensely for over a centuryThe techniques involved in their analysis and the variety of their applications both continue to grow. This book is an admirably comprehensive and lucid account of the topic. It includes some very recent developments in which the author has played a major role. This will be a valuable resource for researchers and an excellent text for a graduate course.' Rajendra Bhatia, Ashoka University
'The opening notes of this symphony of ideas were written by Schur in 1911. Schoenberg, Loewner, Rudin, Herz, Hiai, FitzGerald, Jain, Guillot, Rajaratnam, Belton, Putinar, and others composed new themes and variations. Now, Khare has orchestrated a masterwork that includes his own harmonies in an elegant synthesis. This is a work of impressive scholarship.' Roger Horn, University of Utah, Retired
Apoorva Khare is an Associate Professor of Mathematics at IISc Bangalore. Following a PhD from University of Chicago, he worked at Yale University and Stanford University for eight years. He is a Ramanujan Fellow and Swarnajayanti Fellow of DST, India, with previous support from DARPA, the American Institute of Mathematics (via NSF), and ICMS, UK. Khare has been invited as a Plenary speaker at the leading global conferences in matrix theory and combinatorics: ILAS and FPSAC; and Sectional speaker in the quadrennial leading conferences in Asia (AMC2021) and the Americas (MCA2017).
SKU NGR9781108792042
ISBN 13 9781108792042
ISBN 10 1108792049
Title Matrix Analysis and Entrywise Positivity Preservers
Author Apoorva Khare
Series London Mathematical Society Lecture Note Series
Condition New
Binding Type Paperback
Publisher Cambridge University Press
Year published 2022-03-31
Number of pages 300
Cover note Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
Note This is a new book - be the first to read this copy. With untouched pages and a perfect binding, your brand new copy is ready to be opened for the first time