Linear Algebra and Its Applications Paperback David C. Lay

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Book Title
Linear Algebra and Its Applications Paperback David C. Lay
ISBN
9780321287137
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Product Identifiers

Publisher
Addison Wesley
ISBN-10
0321287134
ISBN-13
9780321287137
eBay Product ID (ePID)
45586491

Product Key Features

Number of Pages
576 Pages
Publication Name
Linear Algebra and Its Applications
Language
English
Publication Year
2005
Subject
Algebra / Linear, Algebra / General
Features
Revised
Type
Textbook
Author
David C. Lay
Subject Area
Mathematics
Format
Trade Paperback

Dimensions

Item Height
0.9 in
Item Weight
38.6 Oz
Item Length
8 in
Item Width
9.4 in

Additional Product Features

Edition Number
3
Intended Audience
College Audience
LCCN
2005-042186
Dewey Edition
23
Illustrated
Yes
Dewey Decimal
512.5
Table Of Content
Chapter 1 Linear Equations in Linear Algebra INTRODUCTORY EXAMPLE: Linear Models in Economics and Engineering 1.1 Systems of Linear Equations 1.2 Row Reduction and Echelon Forms 1.3 Vector Equations 1.4 The Matrix Equation Ax = b 1.5 Solution Sets of Linear Systems 1.6 Applications of Linear Systems 1.7 Linear Independence 1.8 Introduction to Linear Transformations 1.9 The Matrix of a Linear Transformation 1.10 Linear Models in Business, Science, and Engineering Supplementary Exercises Chapter 2 Matrix Algebra INTRODUCTORY EXAMPLE: Computer Models in Aircraft Design 2.1 Matrix Operations 2.2 The Inverse of a Matrix 2.3 Characterizations of Invertible Matrices 2.4 Partitioned Matrices 2.5 Matrix Factorizations 2.6 The Leontief Input=Output Model 2.7 Applications to Computer Graphics 2.8 Subspaces of R^n 2.9 Dimension and Rank Supplementary Exercises Chapter 3 Determinants INTRODUCTORY EXAMPLE: Determinants in Analytic Geometry 3.1 Introduction to Determinants 3.2 Properties of Determinants 3.3 Cramer's Rule, Volume, and Linear Transformations Supplementary Exercises Chapter 4 Vector Spaces INTRODUCTORY EXAMPLE: Space Flight and Control Systems 4.1 Vector Spaces and Subspaces 4.2 Null Spaces, Column Spaces, and Linear Transformations 4.3 Linearly Independent Sets; Bases 4.4 Coordinate Systems 4.5 The Dimension of a Vector Space 4.6 Rank 4.7 Change of Basis 4.8 Applications to Difference Equations 4.9 Applications to Markov Chains Supplementary Exercises Chapter 5 Eigenvalues and Eigenvectors INTRODUCTORY EXAMPLE: Dynamical Systems and Spotted Owls 5.1 Eigenvectors and Eigenvalues 5.2 The Characteristic Equation 5.3 Diagonalization 5.4 Eigenvectors and Linear Transformations 5.5 Complex Eigenvalues 5.6 Discrete Dynamical Systems 5.7 Applications to Differential Equations 5.8 Iterative Estimates for Eigenvalues Supplementary Exercises Chapter 6 Orthogonality and Least Squares INTRODUCTORY EXAMPLE: Readjusting the North American Datum 6.1 Inner Product, Length, and Orthogonality 6.2 Orthogonal Sets 6.3 Orthogonal Projections 6.4 The Gram-Schmidt Process 6.5 Least-Squares Problems 6.6 Applications to Linear Models 6.7 Inner Product Spaces 6.8 Applications of Inner Product Spaces Supplementary Exercises Chapter 7 Symmetric Matrices and Quadratic Forms INTRODUCTORY EXAMPLE: Multichannel Image Processing 7.1 Diagonalization of Symmetric Matrices 7.2 Quadratic Forms 7.3 Constrained Optimization 7.4 The Singular Value Decomposition 7.5 Applications to Image Processing and Statistics Supplementary Exercises ONLINE ONLY Chapter 8 The Geometry of Vector Spaces INTRODUCTORY EXAMPLE: The Platonic Solids 8.1 Affine Combinations 8.2 Affine Independence 8.3 Convex Combinations 8.4 Hyperplanes 8.5 Polytopes 8.6 Curves and Surfaces Supplementary Exercises ONLINE ONLY Chapter 9 Optimization INTRODUCTORY EXAMPLE: The Berlin Airlift 9.1 Matrix Games 9.2 Linear Programming Geometric Method 9.3 Linear Programming Simplex Method 9.4 Duality Supplementary Exercises Appendices A Uniqueness of the Reduced Echelon Form B Complex Numbers Glossary Answers to Odd-Numbered Exercises Index
Edition Description
Revised edition
Synopsis
Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text so that when discussed in the abstract, these concepts are more accessible.
LC Classification Number
QA184.2.L39 2006

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