Linear Algebra
(Sprache: Englisch)
Linear Algebra: Ideas and Applications, Third Edition has been updated and revised, but its parallel structure (abstract concepts are introduced along with computational) and concepts remain intact. The book covers a number of applications of linear algebra...
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Linear Algebra: Ideas and Applications, Third Edition has been updated and revised, but its parallel structure (abstract concepts are introduced along with computational) and concepts remain intact. The book covers a number of applications of linear algebra and features a unique treatment of vector spaces, proofs, and computations.
Klappentext zu „Linear Algebra “
This expanded new edition presents a thorough and up-to-date introduction to the study of linear algebraLinear Algebra, Third Edition provides a unified introduction to linear algebra while reinforcing and emphasizing a conceptual and hands-on understanding of the essential ideas. Promoting the development of intuition rather than the simple application of methods, the book successfully helps readers to understand not only how to implement a technique, but why its use is important.The book outlines an analytical, algebraic, and geometric discussion of the provided definitions, theorems, and proofs. For each concept, an abstract foundation is presented together with its computational output, and this parallel structure clearly and immediately illustrates the relationship between the theory and its appropriate applications. The Third Edition also features:A new chapter on generalized eigenvectors and chain bases with coverage of the Jordan form and the Cayley-Hamilton theoremA new chapter on numerical techniques, including a discussion of the condition numberA new section on Hermitian symmetric and unitary matricesAn exploration of computational approaches to finding eigenvalues, such as the forward iteration, reverse iteration, and the QR methodAdditional exercises that consist of application, numerical, and conceptual questions as well as true-false questionsIlluminating applications of linear algebra are provided throughout most parts of the book along with self-study questions that allow the reader to replicate the treatments independently of the book. Each chapter concludes with a summary of key points, and most topics are accompanied by a "Computer Projects" section, which contains worked-out exercises that utilize the most up-to-date version of MATLAB(r). A related Web site features Maple translations of these exercises as well as additional supplemental material.Linear Algebra, Third Edition is an excellent undergraduate-level textbook for courses in
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linear algebra. It is also a valuable self-study guide for professionals and researchers who would like a basic introduction to linear algebra with applications in science, engineering, and computer science.
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Linear Algebra: Ideas and Applications, Third Edition has been updated and revised, but its parallel structure (abstract concepts are introduced along with computational) and concepts remain intact. The book covers a number of applications of linear algebra and features a unique treatment of vector spaces, proofs, and computations. The text explores linear algebra using an approach that introduces abstract concepts as they are needed to fully understand the computations.
Inhaltsverzeichnis zu „Linear Algebra “
PrefaceFeatures of the Text
1. Systems of Linear Equations
The Space R¯n
Linear Combinations and Linear Dependence
What Is a Vector Space?
Why Prove Anything?
True-False Questions
Exercises
Exercises
Self-Study Questions
Exercises
Rank: The Maximum Number of Linearly Independent Equations
True-False Questions
Exercises
Exercises
Self-Study Questions
Exercises
Spanning in Polynomial Spaces
Computational Issues: Pivoting
True-False Questions
Exercises
Computational Issues: Flops
Exercises
Self-Study Questions
Exercises
Subspaces
Subspaces of Functions
True-False Questions
Exercises
Exercises
Self-Study Questions
Exercises
Chapter Summary
2. Linear Independence and Dimension
Bases for the Column Space
Testing Functions for Independence
True-False Questions
Exercises
True-False Questions
Exercises
Exercises
Self-Study Questions
Exercises
Self-Study Questions
Exercises
Self-Study Questions
Exercises
Exercises
Bases for the Row Space
Rank-Nullity Theorem
Computational Issues: Computing Rank
True-False Questions
Exercises
Chapter Summary
3. Linear Transformations
True-False Questions
Exercises
Self-Study Questions
Exercises
Partitioned Matrices
Computational Issues: Parallel Computing
True-False Questions
Exercises
Self-Study Questions
Exercises
Computational Issues: Reduction vs. Inverses
True-False Questions
Exercises
Ill Conditioned Systems
Exercises
Self-Study Questions
Exercises
Exercises
Exercises
Coordinates
Application to Differential Equations
Isomorphism
Invertible Linear Transformations
True-False Questions
Exercises
Chapter Summary
4. Determinants
True-False Questions
Exercises
Uniqueness of the Determinant
True-False Questions
Exercises
Self-Study Questions
Exercises
Cramer's Rule
True-False
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Questions
Exercises 273
Chapter Summary
5. Eigenvectors and Eigenvalues
True-False Questions
Exercises
Exercises
Powers of Matrices
True-False Questions
Exercises
Self-Study Questions
Exercises
Complex Vector Spaces
Exercises
Exercises
Chapter Summary
6. Orthogonality
Orthogonal/Orthonormal Bases and Coordinates
True-False Questions
Exercises
Self-Study Questions
Exercises
The QR Decomposition 334
Uniqueness of the QR-factoriaition
True-False Questions
Exercises
Exercises
Exercises
Exercises
Householder Matrices
True-False Questions
Exercises
Exercises
Exercises
Exercises
The Spectral Theorem
The Principal Axis Theorem
True-False Questions
Exercises
Exercises
Application of the SVD to Least-Squares Problems
True-False Questions
Exercises
Computing the SVD Using Householder Matrices
Diagonalizing Symmetric Matrices Using Householder Matrices
True-False Questions
Exercises
Chapter Summary
7. Generalized Eigenvectors
Exercises
Jordan Form
True-False Questions
Exercises
The Cayley-Hamilton Theorem
Chapter Summary
8. Numerical Techniques
Norms
Condition Number
Least Squares
Exercises
Iteration
The QR Method
Exercises
Chapter Summary
Answers and Hints
Index
Exercises 273
Chapter Summary
5. Eigenvectors and Eigenvalues
True-False Questions
Exercises
Exercises
Powers of Matrices
True-False Questions
Exercises
Self-Study Questions
Exercises
Complex Vector Spaces
Exercises
Exercises
Chapter Summary
6. Orthogonality
Orthogonal/Orthonormal Bases and Coordinates
True-False Questions
Exercises
Self-Study Questions
Exercises
The QR Decomposition 334
Uniqueness of the QR-factoriaition
True-False Questions
Exercises
Exercises
Exercises
Exercises
Householder Matrices
True-False Questions
Exercises
Exercises
Exercises
Exercises
The Spectral Theorem
The Principal Axis Theorem
True-False Questions
Exercises
Exercises
Application of the SVD to Least-Squares Problems
True-False Questions
Exercises
Computing the SVD Using Householder Matrices
Diagonalizing Symmetric Matrices Using Householder Matrices
True-False Questions
Exercises
Chapter Summary
7. Generalized Eigenvectors
Exercises
Jordan Form
True-False Questions
Exercises
The Cayley-Hamilton Theorem
Chapter Summary
8. Numerical Techniques
Norms
Condition Number
Least Squares
Exercises
Iteration
The QR Method
Exercises
Chapter Summary
Answers and Hints
Index
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Autoren-Porträt von Richard C. Penney
Richard C. Penney, PhD, is Professor in the Department of Mathematics and Director of the Mathematics/Statistics Actuarial Science Program at Purdue University. Dr. Penney is the author of numerous journal articles and has received several major teaching awards.
Bibliographische Angaben
- Autor: Richard C. Penney
- 2008, 3. Aufl., 504 Seiten, Maße: 23,8 cm, Gebunden, Englisch
- Verlag: Wiley & Sons
- ISBN-10: 0470178841
- ISBN-13: 9780470178843
Sprache:
Englisch
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