Matrix Analysis and Entrywise Positivity Preservers

The book is the first to systematically develop the theoretical foundations of the entrywise calculus, focusing on entrywise operations of matrices and kernels with additional structure that preserve positive semidefiniteness. It is designed as an introduction for students and presents an in-depth and comprehensive view of the subject, including structural results, historical connections, and recent connections to combinatorics and Schur polynomials.

Format: Paperback / softback
Length: 300 pages
Publication date: 31 March 2022
Publisher: Cambridge University Press

Throughout the 20th century,matrices and kernels with positivity structures,and the question of entrywise functions preserving them,have been extensively studied,with a recent surge of interest in connection to high-dimensional covariance estimation. This groundbreaking book is the first to systematically establish the theoretical foundations of the entrywise calculus,focusing on entrywise operations,or transforms,of matrices and kernels with additional structure that preserve positive semidefiniteness. Designed as an introduction for students,it offers an in-depth and comprehensive exploration of the subject,spanning from early results to recent advancements. Topics covered 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. Authored by the course instructor,this book is meticulously structured as lecture notes,including exercises for students,while also serving as a comprehensive reference text for experts.

Weight: 516g
Dimension: 153 x 228 x 19 (mm)
ISBN-13: 9781108792042
Edition number: New ed