Linear Algebra and Its Applications, 6th edition
Your access includes:
 Search, highlight, and take notes
 Easily create flashcards
 Use the app for access anywhere
 14day refund guarantee
$10.99per month
4month term, pay monthly or pay $43.96
Learn more, spend less

Study simpler and faster
Use flashcards and other study tools in your eTextbook

Watch and learn
Videos & animations bring concepts to life

Listen on the go
Learn how you like with full eTextbook audio

Special partners and offers
Enjoy perks from special partners and offers for students

Find it fast
Quickly navigate your eTextbook with search
Overview
Linear Algebra and Its Applications is a contemporary introduction with broad, relevant applications of concepts and skills for your future career. In most linear algebra texts, the early stages of the course are relatively easy as material is presented in a familiar concrete setting, but students sometimes hit a wall when abstract concepts are introduced. Certain fundamental concepts such as linear independence, vector space and linear transformations require time to digest, and your grasp of them is essential to succeed in the course. To address this, the authors make these concepts more accessible by introducing them early in a familiar, concrete R^{n} setting, developing them gradually, and returning to them throughout the text so that you can understand them when they are discussed in the abstract. The 6th Edition offers new material, examples and online resources, along with new topics, vignettes and applications.
Published by Pearson (July 10th 2020)  Copyright © 2021
ISBN13: 9780136880929
Subject: Advanced Math
Category: Linear Algebra
Overview
 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
 Projects
 Supplementary Exercises
 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
 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
 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 Change of Basis
 4.7 Digital Signal Processing
 4.8 Applications to Difference Equations
 Projects
 Supplementary Exercises
 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
 Orthogonality and Least Squares
 Introductory Example: The North American Datum and GPS Navigation
 6.1 Inner Product, Length, and Orthogonality
 6.2 Orthogonal Sets
 6.3 Orthogonal Projections
 6.4 The Gram–Schmidt Process
 6.5 LeastSquares Problems
 6.6 Machine Learning and Linear Models
 6.7 Inner Product Spaces
 6.8 Applications of Inner Product Spaces
 Projects
 Supplementary Exercises
 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
 Projects
 Supplementary Exercises
 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
 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
 FiniteState Markov Chains (Online Only)
 Introductory Example: Googling Markov Chains
 10.1 Introduction and Examples
 10.2 The SteadyState Vector and Google's PageRank
 10.3 Communication Classes
 10.4 Classification of States and Periodicity
 10.5 The Fundamental Matrix
 10.6 Markov Chains and Baseball Statistics
Appendices
A. Uniqueness of the Reduced Echelon Form
B. Complex Numbers
Your questions answered
When you purchase an eTextbook subscription, it will last 4 months. You can renew your subscription by selecting Extend subscription on the Manage subscription page in My account before your initial term ends.
If you extend your subscription, we'll automatically charge you every month. If you made a one‑time payment for your initial 4‑month term, you'll now pay monthly. To make sure your learning is uninterrupted, please check your card details.
To avoid the next payment charge, select Cancel subscription on the Manage subscription page in My account before the renewal date. You can subscribe again in the future by purchasing another eTextbook subscription.
When you purchase a Channels subscription it will last 1 month, 3 months or 12 months, depending on the plan you chose. Your subscription will automatically renew at the end of your term unless you cancel it.
We use your credit card to renew your subscription automatically. To make sure your learning is uninterrupted, please check your card details.