Matrix Analysis and Entrywise Positivity Preservers: 471 (London Mathematical Society Lecture Note Series, Series Number 471) - Softcover

Khare, Apoorva

9781108792042: Matrix Analysis and Entrywise Positivity Preservers: 471 (London Mathematical Society Lecture Note Series, Series Number 471)

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ISBN 10: 1108792049 ISBN 13: 9781108792042

Publisher: Cambridge University Press, 2022

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These self-contained lecture notes develop classical and modern results on positive matrices and kernels, and on transforms preserving them.

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About the Author

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).

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Publisher: Cambridge University Press
Publication date: 2022
Language: English
ISBN 10: 1108792049
ISBN 13: 9781108792042
Binding: Paperback
Number of pages: 316

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Matrix Analysis and Entrywise Positivity Preservers

Khare, Apoorva

Published by Cambridge University Press, 2022

ISBN 10: 1108792049 ISBN 13: 9781108792042

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Matrix Analysis and Entrywise Positivity Preservers

Khare, Apoorva

Published by Cambridge University Press, 2022

ISBN 10: 1108792049 ISBN 13: 9781108792042

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Matrix Analysis and Entrywise Positivity Preservers (Paperback)

Apoorva Khare

Published by Cambridge University Press, Cambridge, 2022

ISBN 10: 1108792049 ISBN 13: 9781108792042

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Paperback. Condition: new. Paperback. 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. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9781108792042

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