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Foundations of Free Noncommutative Function Theory

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Foundations of Free Noncommutative Function Theory Synopsis

In this book the authors develop a theory of free noncommutative functions, in both algebraic and analytic settings. Such functions are defined as mappings from square matrices of all sizes over a module (in particular, a vector space) to square matrices over another module, which respect the size, direct sums, and similarities of matrices. Examples include, but are not limited to, noncommutative polynomials, power series, and rational expressions.

Motivation and inspiration for using the theory of free noncommutative functions often comes from free probability. An important application area is dimensionless matrix inequalities; these arise, e.g., in various optimization problems of system engineering. Among other related areas are those of polynomial identities in rings, formal languages and finite automata, quasideterminants, noncommutative symmetric functions, operator spaces and operator algebras, quantum control.

About This Edition

ISBN: 9781470416973
Publication date:
Author: Dmitry S KaliuzhnyiVerbovetskyi, V Vinnikov
Publisher: American Mathematical Society
Format: Hardback
Pagination: 183 pages
Series: Mathematical Surveys and Monographs
Genres: Algebraic geometry
Topology
Probability and statistics
Algebra