Foundations of Free Noncommutative Function Theory (Mathematical Surveys and Monographs) - Hardcover

Kaliuzhnyi-Verbovetskyi, Dmitry S.; Vinnikov, Victor

 
9781470416973: Foundations of Free Noncommutative Function Theory (Mathematical Surveys and Monographs)
Hardcover
ISBN 10: 1470416972 ISBN 13: 9781470416973
Publisher: American Mathematical Society, 2014

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.

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About the Author

Dmitry S. Kaliuzhnyi-Verbovetskyi, Drexel University, Philadelphia, PA, USA.

Victor Vinnikov, Ben Gurion University of the Negev, Beer Sheva, Israel.

"About this title" may belong to another edition of this title.

Publisher
American Mathematical Society
Publication date
2014
Language
English
ISBN 10 
1470416972
ISBN 13 
9781470416973
Binding
Hardcover
Number of pages
183