An Introduction to Linear Algebra and Tensors

Nonfiction, Science & Nature, Mathematics, Algebra
Cover of the book An Introduction to Linear Algebra and Tensors by M. A. Akivis, V. V. Goldberg, Dover Publications
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: M. A. Akivis, V. V. Goldberg ISBN: 9780486148786
Publisher: Dover Publications Publication: July 25, 2012
Imprint: Dover Publications Language: English
Author: M. A. Akivis, V. V. Goldberg
ISBN: 9780486148786
Publisher: Dover Publications
Publication: July 25, 2012
Imprint: Dover Publications
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Dover Publications

Cover of the book The Scientific Papers of James Clerk Maxwell, Vol. I by M. A. Akivis, V. V. Goldberg
Cover of the book The Garden of Heaven by M. A. Akivis, V. V. Goldberg
Cover of the book Gilbert's Table Magic by M. A. Akivis, V. V. Goldberg
Cover of the book Everyday Fashions of the Fifties As Pictured in Sears Catalogs by M. A. Akivis, V. V. Goldberg
Cover of the book Basic Concepts in Modern Mathematics by M. A. Akivis, V. V. Goldberg
Cover of the book Nostradamus and His Prophecies by M. A. Akivis, V. V. Goldberg
Cover of the book Decorative Origami Boxes by M. A. Akivis, V. V. Goldberg
Cover of the book Mendel's Principles of Heredity by M. A. Akivis, V. V. Goldberg
Cover of the book Logic in Elementary Mathematics by M. A. Akivis, V. V. Goldberg
Cover of the book Early Black American Writers by M. A. Akivis, V. V. Goldberg
Cover of the book Easy-to-Build Birdhouses by M. A. Akivis, V. V. Goldberg
Cover of the book Braiding and Knotting by M. A. Akivis, V. V. Goldberg
Cover of the book Dimensional Analysis by M. A. Akivis, V. V. Goldberg
Cover of the book Fundamentals of the Theory of Plasticity by M. A. Akivis, V. V. Goldberg
Cover of the book Paul Morphy and the Evolution of Chess Theory by M. A. Akivis, V. V. Goldberg
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy