Elementary Linear Algebra, 10th Edition

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  • Edition: 10th
  • Format: Hardcover
  • Copyright: 2010-03-01
  • Publisher: Wiley
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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 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
The Geometry of Linear Systems
Cross Product * Chapter Summary
General Vector Spaces
Real Vector Spaces
Linear Independence
Coordinates and Basis
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
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
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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