Linear Algebra and Its Applications, Global Edition

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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9781292351216 Corporate Finance, Global Edition, 5th Edition
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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 ℝⁿ
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