Vector Spaces And Tensor Algebras
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| Author | : Takeo Yokonuma |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 148 |
| Release | : 1992 |
| Genre | : Mathematics |
| ISBN | : 9780821827963 |
This book explains, as clearly as possible, tensors and such related topics as tensor products of vector spaces, tensor algebras, and exterior algebras. You will appreciate Yokonuma's lucid and methodical treatment of the subject. This book is useful in undergraduate and graduate courses in multilinear algebra. Tensor Spaces and Exterior Algebra begins with basic notions associated with tensors. to facilitate understanding of the definitions, Yokonuma often presents two or more different ways of describing one object. Next, the properties and applications of tensors are developed, including the classical definition of tensors and the description of relative tensors. Also discussed are the algebraic foundations of tensor calculus and applications of exterior algebra to determinants and to geometry. This book closes with an examination of algebraic systems with bilinear multiplication. in particular, Yokonuma discusses the theory of replicas of Chevalley and several properties of Lie algebras deduced from them.
| Author | : Richard L. Bishop |
| Publisher | : Courier Corporation |
| Total Pages | : 290 |
| Release | : 2012-04-26 |
| Genre | : Mathematics |
| ISBN | : 0486139239 |
DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div
| Author | : Mikhail Itskov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 253 |
| Release | : 2009-04-30 |
| Genre | : Technology & Engineering |
| ISBN | : 3540939075 |
There is a large gap between engineering courses in tensor algebra on one hand, and the treatment of linear transformations within classical linear algebra on the other. This book addresses primarily engineering students with some initial knowledge of matrix algebra. Thereby, mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises provided in the book are accompanied by solutions enabling autonomous study. The last chapters deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and might therefore be of high interest for PhD-students and scientists working in this area.
| Author | : M. A. Akivis |
| Publisher | : Courier Corporation |
| Total Pages | : 196 |
| Release | : 2012-07-25 |
| Genre | : Mathematics |
| ISBN | : 0486148785 |
Eminently 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 | : Karen R. Strung |
| Publisher | : Springer Nature |
| Total Pages | : 322 |
| Release | : 2020-12-15 |
| Genre | : Mathematics |
| ISBN | : 3030474658 |
This 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 | : Øyvind Grøn |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 351 |
| Release | : 2011-08-30 |
| Genre | : Science |
| ISBN | : 1461407060 |
This book provides an introduction to the theory of relativity and the mathematics used in its processes. Three elements of the book make it stand apart from previously published books on the theory of relativity. First, the book starts at a lower mathematical level than standard books with tensor calculus of sufficient maturity to make it possible to give detailed calculations of relativistic predictions of practical experiments. Self-contained introductions are given, for example vector calculus, differential calculus and integrations. Second, in-between calculations have been included, making it possible for the non-technical reader to follow step-by-step calculations. Thirdly, the conceptual development is gradual and rigorous in order to provide the inexperienced reader with a philosophically satisfying understanding of the theory. The goal of this book is to provide the reader with a sound conceptual understanding of both the special and general theories of relativity, and gain an insight into how the mathematics of the theory can be utilized to calculate relativistic effects.
| Author | : Thomas Scott Blyth |
| Publisher | : |
| Total Pages | : 376 |
| Release | : 1990 |
| Genre | : Mathematics |
| ISBN | : |
This textbook provides a self-contained course on the basic properties of modules and their importance in the theory of linear algebra. The first 11 chapters introduce the central results and applications of the theory of modules. Subsequent chapters deal with advanced linear algebra, including multilinear and tensor algebra, and explore such topics as the exterior product approach to the determinants of matrices, a module-theoretic approach to the structure of finitely generated Abelian groups, canonical forms, and normal transformations. Suitable for undergraduate courses, the text now includes a proof of the celebrated Wedderburn-Artin theorem which determines the structure of simple Artinian rings.
| Author | : Adam Marsh |
| Publisher | : World Scientific |
| Total Pages | : 301 |
| Release | : 2017-11-27 |
| Genre | : Science |
| ISBN | : 9813233931 |
This unique book complements traditional textbooks by providing a visual yet rigorous survey of the mathematics used in theoretical physics beyond that typically covered in undergraduate math and physics courses. The exposition is pedagogical but compact, and the emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions, alternative notations and jargon, and relevant facts and theorems. Special attention is given to detailed figures and geometric viewpoints. Certain topics which are well covered in textbooks, such as historical motivations, proofs and derivations, and tools for practical calculations, are avoided. The primary physical models targeted are general relativity, spinors, and gauge theories, with notable chapters on Riemannian geometry, Clifford algebras, and fiber bundles.
| Author | : Ray M. Bowen |
| Publisher | : Springer |
| Total Pages | : 224 |
| Release | : 1976-05-31 |
| Genre | : Mathematics |
| ISBN | : |
To Volume 1 This work represents our effort to present the basic concepts of vector and tensor analysis. Volume 1 begins with a brief discussion of algebraic structures followed by a rather detailed discussion of the algebra of vectors and tensors. Volume 2 begins with a discussion of Euclidean manifolds, which leads to a development of the analytical and geometrical aspects of vector and tensor fields. We have not included a discussion of general differentiable manifolds. However, we have included a chapter on vector and tensor fields defined on hypersurfaces in a Euclidean manifold. In preparing this two-volume work, our intention was to present to engineering and science students a modern introduction to vectors and tensors. Traditional courses on applied mathematics have emphasized problem-solving techniques rather than the systematic development of concepts. As a result, it is possible for such courses to become terminal mathematics courses rather than courses which equip the student to develop his or her understanding further.
| Author | : Steven Roman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 488 |
| Release | : 2007-12-31 |
| Genre | : Mathematics |
| ISBN | : 038727474X |
Covers 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
