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vls/2603nrwcece.visuallibrary.netvdInequalities in matrix algebrasCarlen, Eric1957-VerfasserauttextTextbookxxuXD-USProvidence, Rhode IslandAmerican Mathematical Society[2025]© 20252025monographicengprintxv, 451 Seitenohne Hilfsmittel zu benutzenBandThe 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.Eric Carlen47A6347C1546L6046L5397814704792379781470480264153018513799376179037806441HT031301782Inequalities in matrix algebrasCarlen, Eric, 1957 -Providence, Rhode IslandAmerican Mathematical Society20251 Online-Ressource (xv, 451 Seiten)Online-Ausgabe9781470480257Graduate studies in mathematics251(DE-605)HT004977518https://zbmath.org/802970049HBZ_BIE49HBZ_PAD49HBZ_ULM49HBZ_ULBrda25103120260706082143.02609000ger https://ce.visuallibrary.net//domainresource/static/graphics/connectors/viewerLogo.gif http://193.30.112.129:83/F/?func=find-c&ccl_term=ICS%3D2609000 https://ce.visuallibrary.net/id/1398372 https://ce.visuallibrary.net/i3f/v20/1398372/manifest https://ce.visuallibrary.net/proto_ftsearch/1398372