**Mathematical Surveys and Monographs** 2014; 183 pp; hardcover Volume: 199 ISBN-10: 1-4704-1697-2 ISBN-13: 978-1-4704-1697-3 List Price: US$77 Member Price: US$61.60 Order Code: SURV/199
| 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, and quantum control. Readership Graduate students interested in noncommutative analysis. |