Linear Algebra and Its Applications, Global Edition
Kaup valmöguleikar
Fyrir námskeið í línulegri algebru. Linear Algebra and Its Applications veitir nútímalegan og aðgengilegan grunn að faginu með fjölbreyttum hagnýtum dæmum og hjálpar nemendum að tileinka sér hugtök og færni sem nýtast í framtíðarstarfi. Í hefðbundnum kennslubókum eru fyrstu skref námskeiðsins oft tiltölulega auðveld, þar sem efnið er sett fram á kunnuglegan og áþreifanlegan hátt. Nemendur reka sig þó gjarnan á vegg þegar óhlutbundin hugtök eru kynnt. Það tekur tíma að tileinka sér grundvallarhugtök línulegrar algebru, svo sem línulegt óhæði, vigurrúm og línulegar varpanir, en traustur skilningur á þeim er nauðsynlegur.
For courses in Linear Algebra. Fosters the concepts and skillsneeded for future careers Linear Algebra and ItsApplications offers a modern elementary introduction with broad, relevantapplications. With traditional texts, the early stages of the course arerelatively easy as material is presented in a familiar, concrete setting, butstudents often hit a wall when abstract concepts are introduced. Certainconcepts fundamental to the study of linear algebra (such as linearindependence, vector space, and linear transformations) require time toassimilate — and students' understanding of them is vital.
Lay, Lay, and McDonald make theseconcepts more accessible by introducing them early in a familiar, concrete ℝn setting, developing them gradually, and returning to themthroughout the text so that students can grasp them when they are discussed inthe abstract. The 6th Edition offers exciting new material, examples,and online resources, along with new topics, vignettes, and applications.
Nánar um bókina
- Pearson International Content
- 9781292351223
- 9781292351216
- Page Fidelity (PDF)
- 6
- David C. Lay; Steven R. Lay; Judi J. McDonald
- English
- 2021-08-24
- 100
- 2
- 2
Kaflar
- Title Page
- Copyright
- Dedication
- About the Authors
- Contents
- Applications Index
- Preface
- Get the most out of MyLab Math
- Resources for Success
- A Note to Students
- 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
- 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: Weighing Diamonds
- 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: Discrete-Time Signals and Digital Signal Processing
- 4.1 Vector Spaces and Subspaces
- 4.2 Null Spaces, Column Spaces, Row 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 Applications to 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 Linear Models
- 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 Image Processing 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
- Project
- 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
- Project
- Supplementary Exercises
- Appendixes
- Appendix A: Uniqueness of the Reduced Echelon Form
- Appendix B: Complex Numbers
- Credits
- Glossary
- Answers to Odd-Numbered Exercises
- Index
- A
- B
- C
- D
- E
- F
- G
- H
- I
- J
- K
- L
- M
- N
- O
- P
- Q
- R
- S
- T
- U
- V
- W
- Z
- Advice on Reading Linear Algebra