An Introduction to Linear Algebra and Tensors

by Maks A. Akivis and Vladislav V. Goldberg

Book Overview

The present book, a valuable addition to the English-language literature on linear algebra and tensors, constitutes a lucid, eminently readable and completely elementary introduction to this field of mathematics. A special merit of the book is its free use of tensor notation, in particular the Einstein summation convention. The treatment is virtually self-contained. In fact, the mathematical background assumed on the part of the reader hardly exceeds a smattering of calculus and a casual acquaintance with determinants. The authors begin with linear spaces, starting with basic concepts and ending with topics in analytic geometry. They then treat multilinear forms and tensors (linear and bilinear forms, general definition of a tensor, algebraic operations on tensors, symmetric and antisymmetric tensors, etc.), and linear transformation (again basic concepts, the matrix and multiplication of linear transformations, inverse transformations and matrices, groups and subgroups, etc.). The last chapter deals with further topics in the field: eigenvectors and eigenvalues, matrix ploynomials and the Hamilton-Cayley theorem, reduction of a quadratic form to canonical form, representation of a nonsingular transformation, and more. Each individual section -- there are 25 in all -- contains a problem set, making a total of over 250 problems, all carefully selected and matched. Hints and answers to most of the problems can be found at the end of the book. Dr. Silverman has revised the text and numerous pedagogical and mathematical improvements, and restyled the language so that it is even more readable. With its clear exposition, many relevant and interesting problems, ample illustrations, index and bibliography, this book will be useful in the classroom or for self-study as an excellent introduction to the important subjects of linear algebra and tensors.

• Format: Paperback
• Language: English
• ISBN: 0486635457
• ISBN13: 9780486635453
• Release Date: October 2010
• Publisher: Dover Publications
• Length: 192 Pages
• Weight: 0.50 lbs.
• Dimensions: 0.4" x 5.6" x 8.2"

Customer Reviews

Small introduction to the multilineal algebra

This book is an elementary introduction to the linear Algebra and Tensors. It restricts their study to three dimensions and orthogonal tensors. Their presentation is compact and doesn't introduce a concept that won't be used with posterity in the book. It doesn't follow the limits of a treaty of the lineal algebra, but rather it centers the study of this matter avoiding to enter in messes that are solved in texts more rigorous. You won't find in this text a systematic treatment and complete of the systems of equations lineals, determinants , canonical forms, Etc., but you will be with a very good general concept of the linear algebra along the whole course. Their reading is easy, very didactic, its sections are highly organized and each one of them has a clear objective: no section is unaware to the rest of the book. To read this book you don't need anything. Scarcely you needed something of calculus, and that to understand some examples and does it. If you don't understand in this book the rudiments of the tensors, I believe that you won't understand it in any other one. The book also is full with illustrative examples and problems whose solution will found at the end of the book. This book is a small introduction to the multilineal algebra .