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| HardcoverISBN: | 978-1-4704-1697-3 |
| eBookISBN: | 978-1-4704-2001-7 |
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| Hardcover ISBN: | 978-1-4704-1697-3 |
| Product Code: | SURV/199 |
| List Price: | $82.00 |
| MAA Member Price: | $73.80 |
| AMS Member Price: | $65.60 |
| eBook ISBN: | 978-1-4704-2001-7 |
| Product Code: | SURV/199.E |
| List Price: | $77.00 |
| MAA Member Price: | $69.30 |
| AMS Member Price: | $61.60 |
| Hardcover ISBN: | 978-1-4704-1697-3 |
| eBookISBN: | 978-1-4704-2001-7 |
| Product Code: | SURV/199.B |
| List Price: | $159.00$120.50 |
| MAA Member Price: | $143.10$108.45 |
| AMS Member Price: | $127.20$96.40 |
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Book DetailsMathematical Surveys and MonographsVolume: 199; 2014; 183 ppMSC: Primary 17; 40; 46; 47;
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.ReadershipGraduate students interested in noncommutative analysis.
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Table of Contents
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Chapters
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Chapter 1. Introduction
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Chapter 2. NC functions and their difference-differential calculus
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Chapter 3. Higher order nc functions and their difference-differential calculus
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Chapter 4. The Taylor-Taylor formula
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Chapter 5. NC functions on nilpotent matrices
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Chapter 6. NC polynomials vs. polynomials in matrix entries
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Chapter 7. NC analyticity and convergence of TT series
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Chapter 8. Convergence of nc power series
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Chapter 9. Direct summands extensions of nc sets and nc functions
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Chapter 10. (Some) earlier work on nc functions
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Appendix A. Similarity invariant envelopes and extension of nc functions
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Additional Material
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RequestsReview Copy – for reviewers who would like to review an AMS bookPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
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- Additional Material
- Requests
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.
Graduate students interested in noncommutative analysis.
-
Chapters
-
Chapter 1. Introduction
-
Chapter 2. NC functions and their difference-differential calculus
-
Chapter 3. Higher order nc functions and their difference-differential calculus
-
Chapter 4. The Taylor-Taylor formula
-
Chapter 5. NC functions on nilpotent matrices
-
Chapter 6. NC polynomials vs. polynomials in matrix entries
-
Chapter 7. NC analyticity and convergence of TT series
-
Chapter 8. Convergence of nc power series
-
Chapter 9. Direct summands extensions of nc sets and nc functions
-
Chapter 10. (Some) earlier work on nc functions
-
Appendix A. Similarity invariant envelopes and extension of nc functions
