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Foundations of Free Noncommutative Function Theory

Dmitry S. Kaliuzhnyi-Verbovetskyi
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      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.
      Format: Hardback CONTRIBUTORS: Dmitry S. Kaliuzhnyi-Verbovetskyi EAN: 9781470416973 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2014-12-30 CITY: GENRE: MATHEMATICS / Algebra / General, MATHEMATICS / Geometry / Algebraic, MATHEMATICS / Number Theory WIDTH: 178 cm SPINE:

      Book Themes:

      Algebra, Number theory, Algebraic geometry

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      Dmitry S. Kaliuzhnyi-Verbovetskyi, Drexel University, Philadelphia, PA, USA.Victor Vinnikov, Ben Gurion University of the Negev, Beer Sheva, Israel.
      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.
      Format: Hardback CONTRIBUTORS: Dmitry S. Kaliuzhnyi-Verbovetskyi EAN: 9781470416973 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2014-12-30 CITY: GENRE: MATHEMATICS / Algebra / General, MATHEMATICS / Geometry / Algebraic, MATHEMATICS / Number Theory WIDTH: 178 cm SPINE:

      Book Themes:

      Algebra, Number theory, Algebraic geometry

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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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