Applied Linear Algebra / Edition 1

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This book describes basic methods and algorithms used in modern, real problems likely to be encountered by engineers and scientists - and fosters an understanding of why mathematical techniques work and how they can be derived from first principles. Assumes no previous exposure to linear algebra. Presents applications hand in hand with theory, leading readers through the reasoning that leads to the important results. Provides theorems and proofs where needed. Features abundant exercises after almost every subsection, in a wide range of difficulty. A thorough reference for engineers and scientists.
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Editorial Reviews

From the Publisher

Some Quotes from Reviewers

“The material on the concept of a general vector space, linear independence, basis, etc. is always difficult for students in this course. This book handles it very well. It gives full, clear explanations. The style is very good, clear, and thorough. It should appeal to my students. I like the book very much. It subscribes to the same philosophy of linear algebra as pioneered by Strang some 30 years ago (acknowledged in the introduction) and builds on the Strang books, making things even clearer and adding more topics. I would certainly like to use this book and would recommend it to my colleagues.”

-Bruno Harris, Brown University

“I like the book very much. We will consider it for our linear algebra courses. This is the best new book to appear since the text by Gilbert Strang. It is really modern book, combining, in a masterful, core and applied aspects of linear algebra. This is a very good book written by a very good mathematician and a very good teacher.”

-Juan J. Manfredi, University of Pittsburgh

“In many, if not most, beginning texts of linear algebra, the applications may be collected together in a chapter at the end of the book or in an appendix, leaving any inclusion of this material to the discretion of the instructor. However, Applied Linear Algebra by Olver and Shakiban completely reverses this procedure with a total integration of the application with the abstract theory. The effect on the reader is quite amazing. The reader slowly begins to realize two main points: (1) how applications generally drive the abstract theory, and (2) how the abstract theory can illuminate the applications, and resolve solutions in very striking ways.

This text is easily the best beginning linear algebra text dealing with the applications in an integrated way that I have seen. There is no doubt that this text will be the standard to which all beginning linear algebra texts will be compared. Simply put, this is an absolutely wonderful text!”

-Norman Johnson, University of Iowa

“I lover the style of this book, especially the fact that you could feel the authors’ enthusiasm about the nice mathematics involved in the theory. The examples were very clear and interesting, and they always tried to approach the same problems over and over again as soon sas they had more weapons at their disposal to attack them. I thought this was great, this text introduces the notion of an abstract space very early (still, after Gaussian Elimination) and in a very natural way, then emphasizes along the way over and over again that tremendously. I would absolutely consider this text. I was really taken by the applications and the organization of the materials. I also loved the abundance of exercises and problems.”

-Tamas Wiandt, Rochester Institute of Technology

“This text is very well-written, has lots of examples, and is easy to read and learn from. I’d use it in my Matrix Methods class. There is a good mixture of routine and more advanced examples.”

-James Curry, University of Colorado-Boulder

“I believe the writing style would appeal to my students because of the clarity and the examples, as well as the tone. I am going to consider its use, once I see its final form.”

-Fabio Augusto Miner, Purdue University

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Product Details

  • ISBN-13: 9780131473829
  • Publisher: Pearson
  • Publication date: 12/10/2004
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 736
  • Sales rank: 383,468
  • Product dimensions: 8.20 (w) x 10.10 (h) x 1.20 (d)

Table of Contents

Chapter 1. Linear Algebraic Systems

1.1. Solution of Linear Systems

1.2. Matrices and Vectors

1.3. Gaussian Elimination—Regular Case

1.4. Pivoting and Permutations

1.5. Matrix Inverses

1.6. Transposes and Symmetric Matrices

1.7. Practical Linear Algebra

1.8. General Linear Systems

1.9. Determinants

Chapter 2. Vector Spaces and Bases

2.1. Vector Spaces

2.2. Subspaces

2.3. Span and Linear Independence

2.4. Bases

2.5. The Fundamental Matrix Subspaces

2.6. Graphs and Incidence Matrices

Chapter 3. Inner Products and Norms

3.1. Inner Products

3.2. Inequalities

3.3. Norms

3.4. Positive Definite Matrices

3.5. Completing the Square

3.6. Complex Vector Spaces

Chapter 4. Minimization and Least Squares Approximation

4.1. Minimization Problems

4.2. Minimization of Quadratic Functions

4.3. Least Squares and the Closest Point

4.4. Data Fitting and Interpolation

Chapter 5. Orthogonality

5.1. Orthogonal Bases

5.2. The Gram-Schmidt Process

5.3. Orthogonal Matrices

5.4. Orthogonal Polynomials

5.5. Orthogonal Projections and Least Squares

5.6. Orthogonal Subspaces

Chapter 6. Equilibrium

6.1. Springs and Masses

6.2. Electrical Networks

6.3. Structures

Chapter 7. Linearity

7.1. Linear Functions

7.2. Linear Transformations

7.3. Affine Transformations and Isometries

7.4. Linear Systems

7.5. Adjoints

Chapter 8. Eigenvalues

8.1. Simple Dynamical Systems

8.2. Eigenvalues and Eigenvectors

8.3. Eigenvector Bases and Diagonalization

8.4. Eigenvalues of Symmetric Matrices

8.5. Singular Values

8.6. Incomplete Matrices and the Jordan Canonical Form

Chapter 9. Linear Dynamical Systems

9.1. Basic Solution Methods

9.2. Stability of Linear Systems

9.3. Two-Dimensional Systems

9.4. Matrix Exponentials

9.5. Dynamics of Structures

9.6. Forcing and Resonance

Chapter 10. Iteration of Linear Systems

10.1. Linear Iterative Systems

10.2. Stability

10.3. Matrix Norms

10.4. Markov Processes

10.5. Iterative Solution of Linear Systems

10.6. Numerical Computation of Eigenvalues

Chapter 11. Boundary Value Problems in One Dimension

11.1. Elastic Bars

11.2. Generalized Functions and the Green's Function

11.3. Adjoints and Minimum Principles

11.4. Beams and Splines

11.5. Sturm-Liouville Boundary Value Problems

11.6. Finite Elements

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