Linear Algebra - Ideas and Applications

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
 

Learn foundational and advanced topics in linear algebra with this concise and approachable resource
 
A comprehensive introduction, Linear Algebra: Ideas and Applications, Fifth 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 explicit numerical examples, 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, Fifth Edition also features:
* A new application section on section on Google's Page Rank Algorithm.
* A new application section on pricing long term health insurance at a Continuing Care Retirement Community (CCRC).
* Many other 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(r) code
 
Linear Algebra: Ideas and Applications, Fifth Edition is an excellent undergraduate-level textbook for one or two semester undergraduate courses in mathematics, science, computer science, and engineering. With an emphasis on intuition development, the book is also an ideal self-study reference.

Inhaltsverzeichnis

Preface xi
 
Features of the Text xiii
 
Acknowledgments xvii
 
About the Companion Website xviii
 
1 Systems of Linear Equations 1
 
1.1 The Vector Space of m × n Matrices 1
 
The Space R^n 4
 
Linear Combinations and Linear Dependence 7
 
What Is a Vector Space? 11
 
Why Prove Anything? 15
 
Exercises 16
 
1.1.1 Computer Projects/Exercises/Exercises 22
 
Exercises 24
 
1.1.2 Applications to Graph Theory I 25
 
Exercises 27
 
1.2 Systems 27
 
Rank: The Maximum Number of Linearly Independent Equations 34
 
Exercises 37
 
1.2.1 Computer Projects/Exercises 39
 
Exercises 39
 
1.2.2 Applications to Circuit Theory 40
 
Exercises 44
 
1.3 Gaussian Elimination 46
 
Spanning in Polynomial Spaces 56
 
Computational Issues: Pivoting 59
 
Exercises 60
 
1.3.1 Using tolerances in MATLAB's rref and rank 66
 
Using Tolerances in rref and Rank 66
 
Exercises 67
 
1.3.2 Applications to Traffic Flow 68
 
Exercises 70
 
1.4 Column Space and Nullspace 71
 
Subspaces 74
 
Exercises 82
 
1.4.1 Computer Projects/Exercises 89
 
Exercises 90
 
Chapter Summary 91
 
2 Linear Independence and Dimension 93
 
2.1 The Test for Linear Independence 93
 
Bases for the Column Space 100
 
Testing Functions for Independence 102
 
Exercises 104
 
2.1.1 Computer Projects/Exercises 108
 
Exercises 108
 
2.2 Dimension 109
 
Exercises 118
 
2.2.1 Computer Projects/Exercises 123
 
Exercises 123
 
2.2.2 Applications to Differential Equations 125
 
Exercises 128
 
2.3 Row Space and the Rank-Nullity Theorem 128
 
Bases for the Row Space 130
 
Computational Issues: Computing Rank 138
 
Exercises 140
 
2.3.1 Computer Projects/Exercises 143
 
Exercises 143
 
Chapter Summary 144
 
3 Linear Transformations 147
 
3.1 The Linearity Properties 147
 
Exercises 155
 
3.1.1 Computer Projects/Exercises 160
 
Exercises 161
 
3.2 Matrix Multiplication (Composition) 162
 
Partitioned Matrices 169
 
Computational Issues: Parallel Computing 171
 
Exercises 171
 
3.2.1 Computer Projects/Exercises 177
 
3-D Computer Graphics 177
 
Exercises 177
 
3.2.2 Applications to Graph Theory II 178
 
Exercises 180
 
3.2.3 Computer Projects/Exercises 180
 
Google's Page Rank Algorithm 180
 
Exercises 183
 
3.3 Inverses 184
 
Computational Issues: Reduction versus Inverses 190
 
Exercises 192
 
3.3.1 Computer Projects/Exercises 197
 
Ill-Conditioned Systems 197
 
Exercises 197
 
3.3.2 Applications to Economics: The Leontief Open Model 199
 
Exercises 204
 
3.4 The LU Factorization 205
 
Exercises 213
 
3.4.1 Computer Projects/Exercises 216
 
Exercises 216
 
3.5 The Matrix of a Linear Transformation 217
 
Coordinates 217
 
Application to Differential Equations 225
 
Isomorphism 228
 
Invertible Linear Transformations 229
 
Exercises 231
 
3.5.1 Computer Projects/Exercises 236
 
Graphing in Skewed-Coordinates 236
 
Exercises 236
 
3.5.2 Computer Projects/Exercises 237
 
Pricing Long Term Health Care Insurance 237
 
Exercises 242
 
Chapter Summary

Über den Autor / die Autorin

RICHARD C. PENNEY, PHD is Emeritus Professor in the Department of Mathematics and former Director of the Mathematics/Statistics Actuarial Science Program at Purdue University. He has authored numerous journal articles, received several major teaching awards, and is an active researcher. He received his graduate education at MIT.

Zusammenfassung

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

Learn foundational and advanced topics in linear algebra with this concise and approachable resource

A comprehensive introduction, Linear Algebra: Ideas and Applications, Fifth 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 explicit numerical examples, 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, Fifth Edition also features:
* A new application section on section on Google's Page Rank Algorithm.
* A new application section on pricing long term health insurance at a Continuing Care Retirement Community (CCRC).
* Many other 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(r) code

Linear Algebra: Ideas and Applications, Fifth Edition is an excellent undergraduate-level textbook for one or two semester undergraduate courses in mathematics, science, computer science, and engineering. With an emphasis on intuition development, the book is also an ideal self-study reference.

Produktdetails

• Autoren: Rc Penney, Richard C Penney, Richard C. Penney, Richard C. (Purdue University) Penney, Penney Richard C.
• Verlag: Wiley, John and Sons Ltd
• Sprache: Englisch
• Produktform: Fester Einband
• Erschienen: 30.11.2020
• EAN: 9781119656920
• ISBN: 978-1-119-65692-0
• Seiten: 512
• Themen: Naturwissenschaften, Medizin, Informatik, Technik > Mathematik > Arithmetik, Algebra; Mathematik, Angewandte Mathematik, Lineare Algebra, Mathematics, Linear Algebra, Applied mathematics, Applied Mathematics in Science, Mathematik in den Naturwissenschaften