Inequalities in Matrix Algebras by Eric Carlen
The theory of positive or completely positive maps from one matrix algebra to another is the mathematical theory underlying the quantum mechanics of finite systems, as well as much of quantum information and computing. Inequalities are fundamental to the subject, and a watershed event in its development was the proof of the strong subadditivity of quantum entropy by Lieb and Ruskai. Over the next 50 years, this result has been extended and refined extensively. The development of the mathematical theory accelerated in the 1990s when researchers began to intensively investigate the quantum mechanical notion of ""entanglement"" of vectors in tensor products of Hilbert spaces. Entanglement was identified by Schrodinger as a fundamental aspect of quantum mechanics, and in recent decades questions about entanglement have led to much mathematical progress. What has emerged is a beautiful mathematical theory that has very recently arrived at a mature form. This book is an introduction to that mathematical theory, starting from modest prerequisites. A good knowledge of linear algebra and the basics of analysis and probability are sufficient. In particular, the fundamental aspects of quantum mechanics that are essential for understanding how a number of questions arose are explained from the beginning.-
Analysis
-
Options Pricing and Portfolio Optimization
-
Scrapbook of Complex Curve Theory
- Partial Differential Equations
-
Algebra
-
A Course on the Web Graph
-
Global Analysis
-
Applied Asymptotic Analysis
-
Advanced Modern Algebra
-
A Course in Operator Theory
-
Representations of Finite and Compact Groups
-
Classical and Quantum Computation
-
Toric Varieties
-
Introduction to Analytic and Probabilistic Number Theory
-
Mathematical Methods in Quantum Mechanics
-
Discovering Modern Set Theory, Part 1
-
Differential Geometry, Lie Groups, and Symmetric Spaces
-
Lectures on Elliptic and Parabolic Equations in Sobolev Spaces
-
Riemann Surfaces by Way of Complex Analytic Geometry
-
Advanced Modern Algebra, Parts 1 and 2
-
Introduction to Quantum Groups and Crystal Bases
-
Introduction to the H-Principle
-
A Course in Differential Geometry
-
Measure Theory and Integration
-
Algebraic Number Fields
-
Algebraic Curves and Riemann Surfaces
-
$\textrm {C}^*$-Algebras and Finite-Dimensional Approximations
-
The Calderon Problem
-
Mathematical Foundations of Deep Learning Models and Algorithms
-
Several Complex Variables with Connections to Algebraic Geometry and Lie Groups
-
Function Theory of One Complex Variable
Eric Carlen, Rutgers University, New Brunswick, NJ.
| SKU | Unavailable |
| ISBN 13 | 9781470479237 |
| ISBN 10 | 1470479230 |
| Title | Inequalities in Matrix Algebras |
| Author | Eric Carlen |
| Series | Graduate Studies In Mathematics |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | American Mathematical Society |
| Year published | 2025-09-30 |
| Number of pages | 458 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |