Kaliuzhnyi-Verbovetskyi and Vinnikov present mathematicians, students, academics, and researchers with a theory of free noncommutative functions in algebraic and analytic frameworks. The authors develop their theory over nine chapters, covering a general introduction to noncommutative (NC) functions, NC functions and their difference-differential calculus, higher order NC functions and their calculus, the Taylor-Taylor formula, NC functions on nilpotent matrices, NC polynomials vs. polynomials in matrix entries, convergence of NC power series, and dired summands estensions of NC sets and NC functions. Annotation ©2015 Ringgold, Inc., Portland, OR (protoview.com)
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Dmitry S. Kaliuzhnyi-Verbovetskyi, Drexel University, Philadelphia, PA, USA.
Victor Vinnikov, Ben Gurion University of the Negev, Beer Sheva, Israel.
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Hardback. Zustand: New. 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. Bestandsnummer des Verkäufers LU-9781470416973
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Hardback. Zustand: New. 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. Bestandsnummer des Verkäufers LU-9781470416973
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