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Synopsis
Eminently readable and completely elementary, this treatment begins with linear spaces and ends with analytic geometry. Additional topics include multilinear forms, tensors, linear transformation, eigenvectors and eigenvalues, matrix polynomials, and more. More than 250 carefully chosen problems appear throughout the book, most with hints and answers. 1972 edition.
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From the Back Cover
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 polynomials 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.
Unabridged and unaltered republication of revised English edition originally titled Introductory Linear Algebra, 1972.
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An Introduction to Linear Algebra and Tensors
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An Introduction to Linear Algebra and Tensors
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Introduction to Linear Algebra and Tensors, An
Published by
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ISBN 10: 0486635457
ISBN 13: 9780486635453
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Trade Paperback. Condition: Fine. Edmund V. Gillon, Jr. (illustrator). Light Creasing on Rear Cover; Rear Cover, Spine Lightly Chipped; Slight Yellowing Due to Age. ALSO KNOWN AS: This Dover edition, first published in 1977, is an unabridged and unaltered republication of the revised English edition published by Prentice-Hall, Inc., Englewood Cliffs, N. J., in 1972 under the title Introductory Linear Algebra. REVISED ENGLISH EDITION TRANSLATED AND EDITED BY: Richard A. Silverman. CONTENTS: Editor's Preface 1 Linear Spaces 2 Multilinear Forms and Tensors 3 Linear Transformations 4 Further topics; Selected Hints and Answers; Bibliography; Index. SYNOPSIS: Richard A. Silverman's series of translations of outstanding Russian textbooks and monographs is well-known to people in mathematics, physics and engineering. The present book is another excellent text from this series, a valuable addition to the English-language literature on linear algebra and tensors. It stems from the first four chapters of the Russian author's important work Tensor Calculus, and 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 definitions 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, group and subgroups, etc.). The last chapter deals with further topics in the field: eigenvectors and eigenvalues, matrix polynomials 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 with 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. Size: 8vo - over 7¾" - 9¾" tall. Seller Inventory # 003197
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