Linear Algebra Ideas and Applications.

Detalles Bibliográficos
Autor principal: Penney, Richard C.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2015.
Colección:New York Academy of Sciences Ser.
Temas:
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Intro
  • Linear Algebra
  • Contents
  • Preface
  • Features of the Text
  • Acknowledgments
  • About the Companion Website
  • Chapter 1 Systems of Linear Equations
  • 1.1 The Vector Space of Matrices
  • The Space Rn
  • Linear Combinations and Linear Dependence
  • What Is a Vector Space?
  • Why Prove Anything?
  • Exercises
  • 1.1.1 Computer Projects
  • Exercises
  • 1.1.2 Applications to Graph Theory I
  • Self-Study Questions
  • Exercises
  • 1.2 Systems
  • Rank: The Maximum Number of Linearly Independent Equations
  • Exercises
  • 1.2.1 Computer Projects
  • Exercises
  • 1.2.2 Applications to Circuit Theory
  • Self-Study Questions
  • Exercises
  • 1.3 Gaussian Elimination
  • Spanning in Polynomial Spaces
  • Computational Issues: Pivoting
  • Exercises
  • Computational Issues: Counting Flops
  • 1.3.1 Computer Projects
  • Exercises
  • Applications to Traffic Flow
  • Self-Study Questions
  • Exercises
  • 1.4 Column Space and Nullspace
  • Subspaces
  • Exercises
  • Computer Projects
  • Chapter Summary
  • Chapter 2 Linear Independence and Dimension
  • 2.1 The Test for Linear Independence
  • Bases for the Column Space
  • Testing Functions for Independence
  • Exercises
  • 2.1.1 Computer Projects
  • Exercises
  • 2.2 Dimension
  • Exercises
  • 2.2.1 Computer Projects
  • Exercises
  • 2.2.2 Applications to Differential Equations
  • Exercises
  • 2.3 Row Space and the rank-nullity theorem
  • Bases for the Row Space
  • Summary
  • Computational Issues: Computing Rank
  • Exercises
  • 2.3.1 Computer Projects
  • Exercises
  • Chapter Summary
  • Chapter 3 Linear Transformations
  • 3.1 The Linearity Properties
  • Exercises
  • 3.1.1 Computer Projects
  • Exercises
  • 3.2 Matrix Multiplication (Composition)
  • Partitioned Matrices
  • Computational Issues: Parallel Computing
  • Exercises
  • 3.2.1 Computer Projects
  • Exercises
  • 3.2.2 Applications to Graph Theory II
  • Self-Study Questions
  • Exercises
  • 3.3 Inverses
  • Computational Issues: Reduction versus Inverses
  • Exercises
  • 3.3.1 Computer Projects
  • Exercises
  • 3.3.2 Applications to Economics
  • Self-Study Questions
  • Exercises
  • 3.4 The LU Factorization
  • Exercises
  • 3.4.1 Computer Projects
  • Exercises
  • 3.5 The Matrix of a Linear Transformation
  • Coordinates
  • Application to Differential Equations
  • Isomorphism
  • Invertible Linear Transformations
  • Exercises
  • Computer Projects
  • Exercises
  • Chapter Summary
  • Chapter 4 Determinants
  • 4.1 Definition of the Determinant
  • 4.1.1 The Rest of the Proofs
  • Exercises
  • 4.1.2 Computer Projects
  • 4.2 Reduction and Determinants
  • Uniqueness of the Determinant
  • Exercises
  • 4.2.1 Volume
  • Exercises
  • A Formula for Inverses
  • Exercises
  • Chapter Summary
  • Chapter 5 Eigenvectors and Eigenvalues
  • 5.1 Eigenvectors
  • Exercises
  • 5.1.1 Computer Projects
  • Exercises
  • 5.1.2 Application to Markov Processes
  • Exercises
  • 5.2 Diagonalization
  • Powers of Matrices
  • Exercises
  • 5.2.1 Computer Projects
  • Exercises

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