Linear algebra and its applications

Linear algebra and its applications

For courses in linear algebra.   With traditional linear algebra texts, the course is relatively easy for students during the early stages as material is presented in a familiar, concrete setting. However, when abstract concepts are introduced, students often hit a wall. Instructors seem to agree...

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Detalles Bibliográficos
Otros Autores: Lay, David C., author (author), Lay, Steven R., 1944- author, McDonald, Judith, author
Formato: Libro electrónico
Idioma:Inglés
Publicado: Boston : Pearson 2016.
Edición:Fifth edition, Global edition
Colección:Always learning.
Materias:
Algebras, Linear.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009633339506719
Tabla de Contenidos:
  • Cover
  • Title Page
  • Copyright Page
  • About the Author
  • Contents
  • Preface
  • Acknowledgments
  • 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
  • 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
  • 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
  • Supplementary Exercises
  • Chapter 4 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 Rank
  • 4.7 Change of Basis
  • 4.8 Applications to Difference Equations
  • 4.9 Applications to Markov Chains
  • 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
  • Supplementary Exercises
  • Chapter 6 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 Least-Squares Problems
  • 6.6 Applications to Linear Models
  • 6.7 Inner Product Spaces
  • 6.8 Applications of Inner Product Spaces
  • 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
  • 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
  • Appendixes
  • A Uniqueness of the Reduced Echelon Form
  • B Complex Numbers
  • Glossary
  • Photo Credits.

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