Linear algebra and its applications new edition

Published by Pearson (April 27, 2022) © 2022

David Lay | Steven Lay | Judi McDonald

• Description
• Table of Contents

Learn key concepts of linear algebra to equip yourself in your studies and future career.

Linear Algebra and Its Applications 6 th edition by Steven R. Lay, Judi J. McDonald and David C. Lay is an excellent introductory guide to the principles and foundations of practical linear algebra.

With its learner-friendly approach, the textbook starts with easier material, building confidence by introducing typically challenging concepts early on and gradually developing them. The book revisits those concepts throughout, ensuring you do not become overwhelmed when abstract concepts are introduced, as you progress with your learning.

The latest edition provides new and revised content, with a range of features, including:

• A broad range of introductory vignettes, application examples, and online resources
• New material and topics to consolidate and enhance your understanding of the subject
• New, modernised applications to prepare your learning of the most innovative topics, such as machine learning, Artificial Intelligence, and digital signal processing

With an array of exercises and questions to support your learning, this textbook provides the tools you need to build on your understanding of linear algebra and succeed in your studies.

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9781292351353 Linear Algebra and Its Applications, Global Edition, 6th edition plus MyLab Math with Pearson eText.

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• 9781292351216 Corporate Finance, Global Edition, 5th Edition
• 9781292351285 Corporate Finance, Global Edition, 5th Edition MyLab® Math with Pearson eText

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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.

About the Authors

Preface

A Note to Students

Chapter 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 Input—Output Model
• 2.7 Applications to Computer Graphics
• 2.8 Subspaces of ℝ 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 Gram—Schmidt 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 Programming–Geometric Method
• 9.3 Linear Programming–Simplex 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