Inequalities in Matrix Algebras (Graduate Studies in Mathematics)

Eric Carlen

ISBN 10: 1470480263 / ISBN 13: 9781470480264

Published by American Mathematical Society, 2025

About this Item

Seller Inventory # 409933616

Bibliographic Details

• Title: Inequalities in Matrix Algebras (Graduate Studies in Mathematics)
• Publisher: American Mathematical Society
• Publication Date: 2025
• Language: English
• ISBN 10: 1470480263
• ISBN 13: 9781470480264
• Binding: Soft cover
• Condition: New

About this title

Synopsis

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 Schrödinger 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.