An Introduction to Linear Algebra and Tensors

by Akivis, M. A.; Goldberg, V. V.; Silverman, Richard A.

• ISBN13: 9780486635453
• ISBN10: 0486635457
• Format: Paperback
• Copyright: 2010-10-18
• Publisher: Dover Publications

Summary

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.

Table of Contents

Editor's Preface

Linear Spaces

Basic Concepts

Linear Dependence

Dimension and Bases

Orthonormal Bases

The Scalar Product

The Vector Product

Triple Products

Basis Transformations

Tensor Calculus

Topics in Analytic Geometry

Multilinear Forms and Tensors

Linear Forms

Bilinear Forms

Multilinear Forms

General Definition of a Tensor

Algebraic Operations on Tensors

Symmetric and Antisymmetric Tensors

Linear Transformations

Basic Concepts

The Matrix of a Linear Transformation and Its Determinant

Linear Transformations and Bilinear Forms

Multiplication of Linear Transformations and Matrices

Inverse Transformations and Matrices

The Group of Linear Transformations and Its Subgroups

Further Topics

Eigenvectors and Eigenvalues

The Case of Distinct Eigenvalues

Matrix Polynomials and the Hamilton-Cayley Theorem

Eigenvectors of a Symmetric Transformation

Diagonalization of a Symmetric Transformation

Reduction of a Quadratic Form to Canonical Form

Representation of a Nonsingular Transformation Selected Hints and Answers

Bibliography

Index

Table of Contents provided by Publisher. All Rights Reserved.