Linear Algebra

Ideas and Applications
 
 
John Wiley & Sons Inc (Verlag)
  • 4. Auflage
  • |
  • erschienen am 21. Oktober 2015
  • |
  • 512 Seiten
 
E-Book | PDF mit Adobe DRM | Systemvoraussetzungen
978-1-118-90962-1 (ISBN)
 
Praise for the Third Edition
"This volume is ground-breaking in terms of mathematical texts in that it does not teach from a detached perspective, but instead, looks to show students that competent mathematicians bring an intuitive understanding to the subject rather than just a master of applications."
- Electric Review
A comprehensive introduction, Linear Algebra: Ideas and Applications, Fourth Edition provides a discussion of the theory and applications of linear algebra that blends abstract and computational concepts. With a focus on the development of mathematical intuition, the book emphasizes the need to understand both the applications of a particular technique and the mathematical ideas underlying the technique.
The book introduces each new concept in the context of an explicit numerical example, which allows the abstract concepts to grow organically out of the necessity to solve specific problems. The intuitive discussions are consistently followed by rigorous statements of results and proofs.
Linear Algebra: Ideas and Applications, Fourth Edition also features:
* Two new and independent sections on the rapidly developing subject of wavelets
* A thoroughly updated section on electrical circuit theory
* Illuminating applications of linear algebra with self-study questions for additional study
* End-of-chapter summaries and sections with true-false questions to aid readers with further comprehension of the presented material
* Numerous computer exercises throughout using MATLAB code
Linear Algebra: Ideas and Applications, Fourth Edition is an excellent undergraduate-level textbook for one or two semester courses for students majoring in mathematics, science, computer science, and engineering. With an emphasis on intuition development, the book is also an ideal self-study reference.
4. Auflage
  • Englisch
  • New York
  • |
  • USA
  • Für Beruf und Forschung
  • 4,30 MB
978-1-118-90962-1 (9781118909621)
1118909623 (1118909623)
weitere Ausgaben werden ermittelt
  • 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
  • 5.2.2 Application to Systems of Differential Equations
  • Exercises
  • 5.3 Complex Eigenvectors
  • Complex Vector Spaces
  • Exercises
  • 5.3.1 Computer Projects
  • 5.3 Exercises
  • Chapter Summary
  • Chapter 6 Orthogonality
  • 6.1 The Scalar Product in
  • Orthogonal/Orthonormal Bases and Coordinates
  • Exercises
  • 6.2 Projections: The Gram-Schmidt Process
  • The QR Decomposition
  • Uniqueness of the Factorization
  • Exercises
  • 6.2.1 Computer Projects
  • Exercises
  • 6.3 Fourier Series: Scalar Product Spaces
  • Exercises
  • 6.3.1 Application to Data Compression: Wavelets
  • Exercises
  • 6.3.2 Computer Projects
  • Exercises
  • 6.4 Orthogonal Matrices
  • Householder Matrices
  • Exercises
  • Discrete Wavelet Transform
  • 6.4.1 Computer Projects
  • Exercises
  • 6.5 Least Squares
  • Exercises
  • 6.5.1 Computer Projects
  • Exercises
  • 6.6 Quadratic Forms: Orthogonal Diagonalization
  • The Spectral Theorem
  • The Principal Axis Theorem
  • Exercises
  • 6.6.1 Computer Projects
  • Exercises
  • 6.7 The Singular Value Decomposition (SVD)
  • Application of the SVD to Least-Squares Problems
  • Exercises
  • Computing the SVD Using Householder Matrices
  • Diagonalizing Matrices Using Householder Matrices
  • 6.8 Hermitian Symmetric and Unitary Matrices
  • Exercises
  • Chapter Summary
  • Chapter 7 Generalized Eigenvectors
  • 7.1 Generalized Eigenvectors
  • Exercises
  • 7.2 Chain Bases
  • Jordan Form
  • Exercises
  • The Cayley-Hamilton Theorem
  • Chapter Summary
  • Chapter 8 Numerical Techniques
  • 8.1 Condition Number
  • Norms
  • Condition Number
  • Least Squares
  • Exercises
  • 8.2 Computing Eigenvalues
  • Iteration
  • The QR Method
  • Proof of Theorem 8.3 on page 457
  • Exercises
  • Chapter Summary
  • Answers and Hints
  • Section 1.1 on page 17
  • Section 1.2 on page 38
  • Section 1.2.2 on page 46
  • Section 1.3 on page 63
  • Section 1.4 on page 86
  • Section 2.1 on page 108
  • Section 2.2 on page 123
  • Section 2.2.2 on page 131
  • Section 2.3 page 143
  • Section 3.1 on page 157
  • Section 3.2 on page 173
  • Section 3.3 on page 190
  • Section 3.4 on page 212
  • Section 3.5 on page 230
  • Section 4.1 on page 249
  • Section 4.2 on page 258
  • Section 4.3 on page 268
  • Section 5.1 on page 279
  • Section 5.1.2 on page 285
  • Section 5.2 on page 290
  • Section 5.3 on page 304
  • Section 6.1 page 316
  • Section 6.2 on page 328
  • Section 6.3 on page 341
  • Section 6.4 on page 364
  • Section 6.5 on page 377
  • Section 6.6 on page 392
  • Section 6.7 on page 404
  • Section 6.8 on page 417
  • Section 7.1 on page 429
  • Section 7.2 on page 443
  • Section 8.1 on page 451
  • Index
  • EULA

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