Read and Download eBook Full
Author: Richard L. Bishop
Publisher: Courier Corporation
Published: 2012-04-26
Total Pages: 290
ISBN-13: 0486139239
DOWNLOAD EBOOKDIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div
Author: N.B. Singh
Publisher: N.B. Singh
Published:
Total Pages: 141
ISBN-13:
DOWNLOAD EBOOK"Abstract Algebra: Tensor Products" provides a comprehensive exploration of tensor products within the framework of abstract algebra. Beginning with foundational definitions and universal properties, the book progresses to elucidate their applications across diverse algebraic structures such as modules, vector spaces, and rings. Emphasizing clarity and depth, it navigates through advanced topics including categorical perspectives, functorial properties, and their relevance in fields like quantum mechanics and topology. Through numerous examples, and theoretical insights, this book equips readers with the tools to understand and leverage tensor products as powerful algebraic tools, fostering a deeper appreciation for their role in modern mathematics.
Author: Karen R. Strung
Publisher: Springer Nature
Published: 2020-12-15
Total Pages: 322
ISBN-13: 3030474658
DOWNLOAD EBOOKThis book is directed towards graduate students that wish to start from the basic theory of C*-algebras and advance to an overview of some of the most spectacular results concerning the structure of nuclear C*-algebras. The text is divided into three parts. First, elementary notions, classical theorems and constructions are developed. Then, essential examples in the theory, such as crossed products and the class of quasidiagonal C*-algebras, are examined, and finally, the Elliott invariant, the Cuntz semigroup, and the Jiang-Su algebra are defined. It is shown how these objects have played a fundamental role in understanding the fine structure of nuclear C*-algebras. To help understanding the theory, plenty of examples, treated in detail, are included. This volume will also be valuable to researchers in the area as a reference guide. It contains an extensive reference list to guide readers that wish to travel further.
Author: Philippe Gille
Publisher: Cambridge University Press
Published: 2017-08-10
Total Pages: 431
ISBN-13: 1107156378
DOWNLOAD EBOOKThe first comprehensive modern introduction to central simple algebra starting from the basics and reaching advanced results.
Author: M. A. Akivis
Publisher: Courier Corporation
Published: 2012-07-25
Total Pages: 196
ISBN-13: 0486148785
DOWNLOAD EBOOKEminently readable, completely elementary treatment begins with linear spaces and ends with analytic geometry, covering multilinear forms, tensors, linear transformation, and more. 250 problems, most with hints and answers. 1972 edition.
Author: Steven Roman
Publisher: Springer Science & Business Media
Published: 2007-12-31
Total Pages: 488
ISBN-13: 038727474X
DOWNLOAD EBOOKCovers a notably broad range of topics, including some topics not generally found in linear algebra books Contains a discussion of the basics of linear algebra
Author: Hongyu Guo
Publisher: World Scientific
Published: 2021-06-16
Total Pages: 246
ISBN-13: 9811241031
DOWNLOAD EBOOKTensors have numerous applications in physics and engineering. There is often a fuzzy haze surrounding the concept of tensor that puzzles many students. The old-fashioned definition is difficult to understand because it is not rigorous; the modern definitions are difficult to understand because they are rigorous but at a cost of being more abstract and less intuitive.The goal of this book is to elucidate the concepts in an intuitive way but without loss of rigor, to help students gain deeper understanding. As a result, they will not need to recite those definitions in a parrot-like manner any more. This volume answers common questions and corrects many misconceptions about tensors. A large number of illuminating illustrations helps the reader to understand the concepts more easily.This unique reference text will benefit researchers, professionals, academics, graduate students and undergraduate students.
Author: Sergei Winitzki
Publisher: Sergei Winitzki
Published: 2009-07-30
Total Pages: 286
ISBN-13: 140929496X
DOWNLOAD EBOOKThis is a pedagogical introduction to the coordinate-free approach in basic finite-dimensional linear algebra. The reader should be already exposed to the array-based formalism of vector and matrix calculations. This book makes extensive use of the exterior (anti-commutative, "wedge") product of vectors. The coordinate-free formalism and the exterior product, while somewhat more abstract, provide a deeper understanding of the classical results in linear algebra. Without cumbersome matrix calculations, this text derives the standard properties of determinants, the Pythagorean formula for multidimensional volumes, the formulas of Jacobi and Liouville, the Cayley-Hamilton theorem, the Jordan canonical form, the properties of Pfaffians, as well as some generalizations of these results.
Author: Gilles Pisier
Publisher: Cambridge University Press
Published: 2020-02-27
Total Pages: 495
ISBN-13: 1108479014
DOWNLOAD EBOOKPresents an important open problem on operator algebras in a style accessible to young researchers or Ph.D. students.
Author: Pavel Etingof
Publisher: American Mathematical Soc.
Published: 2016-08-05
Total Pages: 362
ISBN-13: 1470434415
DOWNLOAD EBOOKIs there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.
