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OverviewIn 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. Full Product DetailsAuthor: Dmitry S. Kaliuzhnyi-Verbovetskyi , Victor VinnikovPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: 199 Weight: 0.456kg ISBN: 9781470416973ISBN 10: 1470416972 Pages: 183 Publication Date: 30 December 2014 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Temporarily unavailable  The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you. Table of ContentsIntroduction NC functions and their difference-differential calculus Higher order nc functions and their difference-differential calculus The Taylor-Taylor formula NC functions on nilpotent matrices NC polynomials vs. polynomials in matrix entries NC analyticity and convergence of TT series Convergence of nc power series Direct summands extensions of nc sets and nc functions (Some) earlier work on nc functions Similarity invariant envelopes and extension of nc functions Bibliography IndexReviewsAuthor InformationDmitry S. Kaliuzhnyi-Verbovetskyi, Drexel University, Philadelphia, PA, USA. Victor Vinnikov, Ben Gurion University of the Negev, Beer Sheva, Israel. Tab Content 6Author Website:Countries AvailableAll regions |
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