Linear Algebra and its Applications

ISBN-10: 0201347741
ISBN-13: 9780201347746
Edition: 2nd 2000 (Revised)
Authors: David C. Lay
List price: $109.20
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Book details

List price: $109.20
Edition: 2nd
Copyright year: 2000
Publisher: Addison-Wesley Longman, Incorporated
Publication date: 8/11/1999
Binding: Mixed Media
Pages: 555
Size: 8.19" wide x 9.45" long x 1.02" tall
Weight: 2.838
Language: English

(Each chapter begins with an Introductory Example and ends with Supplementary Exercises.)
Linear Equations In Linear Algebra
Introductory Example: Linear Models in Economics and Engineering
Systems of Linear Equations
Row Reduction and Echelon Forms
Vector Equations
The Matrix Equation Ax = b
Solution Sets of Linear Systems
Linear Independence
Introduction to Linear Transformations
The Matrix of a Linear Transformation
Linear Models in Business, Science, and Engineering
Supplementary Exercises
Matrix Algebra
Introductory Example: Computer Graphics in Automotive Design
Matrix Operations
The Inverse of a Matrix
Characterizations of Invertible Matrices
Partitioned Matrices
Matrix Factorizations
Iterative Solutions of Linear Systems
The Leontief Input-Output Model
Applications to Computer Graphics
Subspaces of Rn
Supplementary Exercises
Introductory Example: Determinants in Analytic Geometry
Introduction to Determinants
Properties of Determinants
Cramer?s Rule, Volume, and Linear Transformations
Supplementary Exercises
Vector Spaces
Introductory Example: Space Flight and Control Systems
Vector Spaces and Subspaces
Null Spaces, Column Spaces, and Linear Transformations
Linearly Independent Sets; Bases
Coordinate Systems
The Dimension of a Vector Space
Change of Basis
Applications to Difference Equations
Applications to Markov Chains
Supplementary Exercises
Eigenvalues and Eigenvectors
Introductory Example: Dynamical Systems and Spotted Owls
Eigenvectors and Eigenvalues
The Characteristic Equation
Eigenvectors and Linear Transformations
Complex Eigenvalues
Discrete Dynamical Systems
Applications to Differential Equations
Iterative Estimates for Eigenvalues
Supplementary Exercises
Orthogonality and Least-Squares
Introductory Example: Readjusting the North American Datum
Inner Product, Length, and Orthogonality
Orthogonal Sets
Orthogonal Projections
The Gram-Schmidt Process
Least-Squares Problems
Applications to Linear Models
Inner Product Spaces
Applications of Inner Product Spaces
Supplementary Exercises
Symmetric Matrices and Quadratic Forms
Introductory Example: Multichannel Image Processing
Diagonalization of Symmetric Matrices
Quadratic Forms
Constrained Optimization
The Singular Value Decomposition
Applications to Image Processing and Statistics
Supplementary Exercises
Uniqueness of the Reduced Echelon Form
Complex Numbers
Answers to Odd-Numbered Exercises

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