David Lay, Steven Lay, Judi McDonald

Linear Algebra and Its Applications, Global Edition

• Broschiertes Buch

Produktbeschreibung

Fosters the concepts and skills needed for future careers Linear Algebra and Its Applications offers a modern elementary introduction with broad, relevant applications. With traditional texts, the early stages of the course are relatively easy as material is presented in a familiar, concrete setting, but students often hit a wall when abstract concepts are introduced. Certain concepts fundamental to the study of linear algebra (such as linear independence, vector space, and linear transformations) require time to assimilate GÇö and students' understanding of them is vital. Lay, Lay, and McDonald make these concepts more accessible by introducing them early in a familiar, concrete setting, developing them gradually, and returning to them throughout the text so that students can grasp them when they are discussed in the abstract. The 6th Edition offers exciting new material, examples, and online resources, along with new topics, vignettes, and applications. Reach every student by pairing this text with MyLab Math MyLabGäó is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab personalizes the learning experience and improves results for each student. MyLab Math should only be purchased when required by an instructor. Please be sure you have the correct ISBN and Course ID. Instructors, contact your Pearson representative for more information. This title is a Pearson Global Edition. The Editorial team at Pearson has worked closely with educators around the world to include content which is especially relevant to students outside the United States. This package includes MyLab. For courses in Linear Algebra.

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Produktdetails

• Verlag: Pearson Education Limited
• 6 ed
• Seitenzahl: 672
• Erscheinungstermin: 4. Februar 2021
• Englisch
• Abmessung: 255mm x 207mm x 32mm
• Gewicht: 1264g
• ISBN-13: 9781292351216
• ISBN-10: 1292351217
• Artikelnr.: 60863031

Autorenporträt

David C. Lay, University of Maryland–College Park Steven R. Lay, Lee University Judi J. McDonald, Washington State University

Inhaltsangabe

About the Authors Preface A Note to StudentsChapter 1 Linear Equations in
LinearAlgebra
* 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
* Projects
* 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 InputOutput Model
* 2.7 Applications to Computer Graphics
* 2.8 Subspaces of n
* 2.9 Dimension and Rank
* Projects
* Supplementary Exercises
Chapter 3 Determinants
* Introductory Example: Random Paths and Distortion
* 3.1 Introduction to Determinants
* 3.2 Properties of Determinants
* 3.3 Cramer's Rule, Volume, and Linear Transformations
* Projects
* Supplementary Exercises
Chapter 4 Vector Spaces
* Introductory Example: Space Flightand 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 Change of Basis
* 4.7 Digital Signal Processing
* 4.8 Applications to Difference Equations
* Projects
* 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
* 5.9 Markov Chains
* Projects
* Supplementary Exercises
Chapter 6 Orthogonality and Least Squares
* Introductory Example: Artificial Intelligence and Machine Learning
* 6.1 Inner Product, Length, and Orthogonality
* 6.2 Orthogonal Sets
* 6.3 Orthogonal Projections
* 6.4 The GramSchmidt Process
* 6.5 Least-Squares Problems
* 6.6 Machine Learning and LinearModels
* 6.7 Inner Product Spaces
* 6.8 Applications of Inner Product Spaces
* Projects
* 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 ImageProcessing and Statistics
* Projects
* Supplementary Exercises
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
* Projects
* Supplementary Exercises
Chapter 9 Optimization
* Introductory Example: The Berlin Airlift
* 9.1 Matrix Games
* 9.2 Linear ProgrammingGeometric Method
* 9.3 Linear ProgrammingSimplex Method
* 9.4 Duality
* Projects
* Supplementary Exercises
Chapter 10 Finite-State Markov Chains(Online Only)
* Introductory Example: Googling Markov Chains
* 10.1 Introduction and Examples
* 10.2 The Steady-State Vector andGoogle's PageRank
* 10.3 Communication Classes
* 10.4 Classification of States andPeriodicity
* 10.5 The Fundamental Matrix
* 10.6 Markov Chains and BaseballStatistics
Appendixes
1. Uniqueness of the Reduced Echelon Form
2. Complex Numbers
Credits Glossary Answers to Odd-Numbered Exercises Index