9781429215213

Linear Algebra A Geometric Approach

by ;
  • ISBN13:

    9781429215213

  • ISBN10:

    1429215216

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 7/30/2010
  • Publisher: W. H. Freeman

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Summary

Linear Algebra: A Geometric Approach, Second Edition, presents the standard computational aspects of linear algebra and includes a variety of intriguing interesting applications that would be interesting to motivate science and engineering students, as well as help mathematics students make the transition to more abstract advanced courses. The text guides students on how to think about mathematical concepts and write rigorous mathematical arguments.

Table of Contents

 
Preface
Foreword to the Instructor
Foreword to the Student
 
Chapter 1. Vectors and Matrices
1. Vectors
2. Dot Product
3. Hyperplanes in Rn
4. Systems of Linear Equations and Gaussian Elimination
5. The Theory of Linear Systems
6. Some Applications
 
Chapter 2.  Matrix Algebra
1. Matrix Operations
2. Linear Transformations: An Introduction
3. Inverse Matrices
4. Elementary Matrices: Rows get Equal Time
5. The Transpose
 
Chapter 3. Vector Spaces
1. Subspaces of  Rn
2. The Four Fundamental Subspaces
3. Linear Independence and Basis
4. Dimension and Its Consequences
5. A Graphic Example
6. Abstract Vector Spaces
 
Chapter 4. Projections and Linear Transformations
1. Inconsistent Systems and Projection
2. Orthogonal Bases
3. The Matrix of a Linear Transformation and the Change-of-Basis Formula
4. Linear Transformations on Abstract Vector Spaces
 
Chapter 5. Determinants
1. Properties of Determinants
2. Cofactors and Cramer’s Rule
3. Signed Area in R2 and Signed Volume in R2
 
Chapter 6. Eigenvalues and Eigenvectors
1. The Characteristic Polynomial
2. Diagonalizability
3. Applications
4. The Spectral Theorem
 
Chapter 7. Further Topics
1. Complex Eigenvalues and Jordan Canonical Form
2. Computer Graphics and Geometry
3. Matrix Exponentials and Differential Equations
 
For Further Reading
Answers to Selected Exercises
List of Blue Boxes
Index

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