Elementary Linear Algebra, 10th Edition

by Howard Anton (Drexel Univ.)

• ISBN13: 9780470458211
• ISBN10: 0470458216
• Edition: 10th
• Format: Hardcover
• Copyright: 2010-03-01
• Publisher: Wiley

Summary

When it comes to learning linear algebra, engineers trust Anton. The tenth edition presents the key concepts and topics along with engaging and contemporary applications. The chapters have been reorganized to bring up some of the more abstract topics and make the material more accessible. More theoretical exercises at all levels of difficulty are integrated throughout the pages, including true/false questions that address conceptual ideas. New marginal notes provide a fuller explanation when new methods and complex logical steps are included in proofs. Small-scale applications also show how concepts are applied to help engineers develop their mathematical reasoning.

Table of Contents

Systems Of Linear Equations And Matrices

Introduction to Systems of Linear Equations

Gaussian Elimination

Matrices and Matrix Operations

Inverses Algebraic Properties of Matrices

Elementary Matrices and a Method for Finding A-1

More on Linear Systems and Invertible Matrices

Diagonal, Triangular, and Symmetric Matrices

Applications of Linear Systems (Traffic flow Electrical Networks Balancing Chemical Equations, Polynomial Interpolation)

Leontief Input-Output Models * Chapter Summary

Determinants

Determinants by Cofactor Expansion

Evaluating Determinants by Row Reduction

Properties of Determinants Adjoint Cramer's Rule * Chapter Summary

Euclidean Vector Spaces

Vectors in 2-space, 3-space, and n-space

Norm, Dot Product, and Distance in Rn

Orthogonality

The Geometry of Linear Systems

Cross Product * Chapter Summary

General Vector Spaces

Real Vector Spaces

Subspaces

Linear Independence

Coordinates and Basis

Dimension

Change of Basis

Row Space, Column Space, and Null Space

Rank, Nullity, and the Fundamental Matrix Spaces

Linear Transformations from Rn to Rm

Properties of Matrix Transformations from Rn to Rm

Geometry of Matrix Operators

Dynamical Systems and Markov Chains * Chapter Summary

Eignvalues And Eigenvectors

Eigenvalues and Eigenvectors

Diagonalization

Complex Vector Spaces

Application to Differential Equations * Chapter Summary

Inner Product Spaces

Inner Products

Angle and Orthogonality in Inner Product Spaces

Orthonormal Bases Gram-Schmidt Process QR - Decomposition

Best Approximation Least Squares

Least Squares Fitting to Data

Fourier Series * Chapter Summary

Diagonalization And Quadratic Forms

Orthogonal Matrices

Orthogonal Diagonalization

Quadratic Forms

Application of Quadratic Forms to Optimization

Hermitian, Unitary, and Normal Matrices * Chapter Summary

Linear Transformations

General Linear Transformations

Isomorphism

Composition and Inverse Transformations

Matrices of General Linear Transformations

Similarity * Chapter Summary

Numerical Methods

Matrix Factorization and LU-Decompositions

The Power Method

Application to Internet Search Engines

Comparison of Procedures for Solving Linear Systems

Singular-Value Decomposition

Application of Singular Value Decomposition to Data Compression * Chapter Summary

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