This expanded new edition presents a thorough and up-to-date introduction to the study of linear algebra
Linear 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:
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A new chapter on generalized eigenvectors and chain bases with coverage of the Jordan form and the Cayley-Hamilton theorem
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A new chapter on numerical techniques, including a discussion of the condition number
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A new section on Hermitian symmetric and unitary matrices
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An exploration of computational approaches to finding eigenvalues, such as the forward iteration, reverse iteration, and the QR method
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Additional exercises that consist of application, numerical, and conceptual questions as well as true-false questions
Illuminating 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 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.
Rezensionen / Stimmen
"Linear Algebra (third edition) is an excellent undergraduate-level textbook for courses in linear algebra. It is also valuable self-study guide for professionals and researches who would like a basic introduction to linear algebra with applications in science, engineering, and computer science." ( Mathematical Review , Issue 2009e) "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, Nov 2008) "This book should make a good text for introductory courses." ( Computing Reviews , September 30, 2008)
Auflage
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Editions-Typ
Illustrationen
Maße
Höhe: 23.8 cm
Breite: 16.4 cm
Dicke: 2.7 cm
Gewicht
ISBN-13
978-0-470-17884-3 (9780470178843)
Schweitzer Klassifikation
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.
Autor*in
Department of Mathematics, Purdue University, Lafayette, Indiana
Preface.
Features 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 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.
