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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 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.
Autorentext
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.
Klappentext
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:
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:
Inhalt
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 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
…