Category: Linear

Linear Algebra and Geometry by Kam-Tim Leung

By Kam-Tim Leung

Linear algebra is now incorporated within the undergraduate curriculum of such a lot universities. it's usually famous that this department of algebra, being much less summary and at once inspired by means of geometry, is simpler to appreciate than another branches and that due to the extensive purposes it's going to learn once attainable. This booklet is an extension of the lecture notes for a direction in algebra and geometry for first-year undergraduates of arithmetic and actual sciences.

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Category: Linear

Lineare Algebra: Eine Einführung für Studienanfänger by Gerd Fischer

By Gerd Fischer

Das seit über 30 Jahren bewährte, einführende Lehrbuch eignet sich als Grundlage für eine zweisemestrige Vorlesung für Studierende der Mathematik, Physik und Informatik. Für einen schnellen und leichteren Einstieg ist das Buch ebenfalls zu verwenden, indem die markierten Abschnitte weggelassen werden. Zentrale Themen sind: Lineare Gleichungssysteme, Eigenwerte und Skalarprodukte. Besonderer Wert wird darauf gelegt, Begriffe zu motivieren, durch Beispiele und durch Bilder zu illustrieren und konkrete Rechenverfahren für die Praxis abzuleiten. Der textual content enthält zahlreiche Übungsaufgaben. Lösungen dazu findet guy in dem von H. Stoppel und B. Griese verfassten "Übungsbuch zur Linearen Algebra ". Zur Motivation der Studierenden enthält das Buch eine Einführung, in der die Bedeutung der Linearen Algebra als Grundlage innerhalb der Mathematik und ihren Anwendungen beschrieben wird.

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Category: Linear

Operator Algebras and Quantum Statistical Mechanics: by Ola Bratteli

By Ola Bratteli

For virtually twenty years, this has been the classical textbook on functions of operator algebra concept to quantum statistical physics. significant alterations within the new version relate to Bose-Einstein condensation, the dynamics of the X-Y version and questions about part transitions.

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Category: Linear

Wave Propagation in Linear and Nonlinear Periodic Media: by A. B. Movchan, M. Brun, N. V. Movchan (auth.), Francesco

By A. B. Movchan, M. Brun, N. V. Movchan (auth.), Francesco Romeo, Massimo Ruzzene (eds.)

Waves and disorder modes in buildings media.- Piezoelectric superlattices and shunted periodic arrays as tunable periodic buildings and metamaterials.- Topology optimization.- Map-based methods for periodic structures.- Methodologies for nonlinear periodic media.​

The contributions during this quantity current either the theoretical heritage and an summary of the state-of-the paintings in wave propagation in linear and nonlinear periodic media in a constant structure. They mix the cloth issued from various engineering purposes, spanning quite a lot of size scale, characterised by way of constructions and fabrics, either man-made and of course happening, that includes geometry, micro-structural and/or fabrics houses that change periodically in area, together with periodically stiffened plates, shells and beam-like in addition to bladed disc assemblies, phononic metamaterials, photonic crystals and ordered granular media. besides linear types and purposes, analytical methodologies for studying and exploiting advanced dynamical phenomena coming up in nonlinear periodic platforms also are presented.​

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Category: Linear

Category: Linear

Max-linear Systems: Theory and Algorithms by Peter Butkovič

By Peter Butkovič

Recent years have noticeable an important upward thrust of curiosity in max-linear concept and methods. as well as supplying the linear-algebraic heritage within the box of tropical arithmetic, max-algebra presents mathematical conception and methods for fixing a number of nonlinear difficulties bobbing up in parts similar to production, transportation, allocation of assets and data processing know-how. it truly is, for this reason, an important subject spanning either natural and utilized mathematical fields.

A welcome advent to the topic of max-plus (tropical) linear algebra, and particularly algorithmic difficulties, Max-linear platforms: conception and Algorithms deals a consolidation of either new and current literature, hence filling a much-needed hole. delivering the basics of max-algebraic thought in a finished and unified shape, as well as extra complex fabric with an emphasis on feasibility and reachability, this booklet offers a couple of new examine effects. subject matters coated variety from max-linear structures and the eigenvalue-eigenvector challenge to periodic habit of matrices, max-linear courses, linear independence, and matrix scaling.

This e-book assumes no past wisdom of max-algebra and masses of the theoryis illustrated with numerical examples, complemented by way of workouts, and observed by way of either useful and theoretical functions. Open difficulties also are verified.

A clean and pioneering method of the subject of Max-linear structures, this e-book will carry a wide-ranging readership, and should be priceless for:

• an individual with uncomplicated mathematical wisdom wishing to benefit crucial max-algebraic principles and strategies

• undergraduate and postgraduate scholars of arithmetic or a comparable measure

• arithmetic researchers

• mathematicians operating in undefined, trade or management

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Category: Linear

Positive Linear Maps of Operator Algebras by Erling Størmer

By Erling Størmer

This quantity, starting off the idea of optimistic maps because it stands this day, displays the speedy development during this region of arithmetic because it was once famous within the Nineties that those purposes of C*-algebras are the most important to the learn of entanglement in quantum thought. the writer, a number one authority at the topic, units out a number of effects formerly unpublished in e-book shape. as well as outlining the homes and buildings of confident linear maps of operator algebras into the bounded operators on a Hilbert house, he publications readers via proofs of the Stinespring theorem and its purposes to inequalities for confident maps.   The textual content examines the maps’ positivity houses, in addition to their linked linear functionals including their density operators. It gains designated sections on extremal optimistic maps and Choi matrices. In sum, this can be a important book that covers a whole spectrum of concerns on the subject of confident linear maps, of which a wide percentage is appropriate and appropriate to today’s quantum details thought. The latter sections of the e-book current the cloth in finite dimensions, whereas the textual content as a complete appeals to a much broader and extra basic readership via conserving the maths as ordinary as attainable all through.

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Category: Linear

An Introduction to Metric Spaces and Fixed Point Theory by Mohamed A. Khamsi

By Mohamed A. Khamsi

Content material:
Chapter 1 creation (pages 1–11):
Chapter 2 Metric areas (pages 13–40):
Chapter three Metric Contraction ideas (pages 41–69):
Chapter four Hyperconvex areas (pages 71–99):
Chapter five “Normal” constructions in Metric areas (pages 101–124):
Chapter 6 Banach areas: advent (pages 125–170):
Chapter 7 non-stop Mappings in Banach areas (pages 171–196):
Chapter eight Metric fastened aspect idea (pages 197–241):
Chapter nine Banach area Ultrapowers (pages 243–271):

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Category: Linear

Pseudo-reductive Groups (New Mathematical Monographs) by Brian Conrad

By Brian Conrad

Pseudo-reductive teams come up certainly within the research of normal delicate linear algebraic teams over non-perfect fields and feature many very important purposes. This self-contained monograph offers a complete remedy of the idea of pseudo-reductive teams and provides their type in a usable shape. The authors current a number of new effects and in addition provide an entire exposition of titties' constitution concept of unipotent teams. They turn out the conjugacy effects (conjugacy of maximal break up tori, minimum pseudo-parabolic subgroups, maximal cut up unipotent subgroups) introduced through Armand Borel and Jacques titties, and in addition provide the Bruhat decomposition, of normal soft attached algebraic teams. Researchers and graduate scholars operating in any comparable sector, equivalent to algebraic geometry, algebraic workforce concept, or quantity thought, will worth this ebook because it develops instruments more likely to be utilized in tackling different difficulties.

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Category: Linear