Cover: Linear Algebra, 2nd Edition by Ted Shifrin; Malcolm Adams

Linear Algebra

Second  Edition©2011  Ted Shifrin; Malcolm Adams

About

Learn how to think about mathematical concepts and write rigorous mathematical arguments.  

Linear Algebra walks you through the standard computational aspects of the subject, using an assortment of intriguing applications designed with science and engineering students like you in mind.

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

Ted Shifrin

Theodore Shifrin is a Professor of Mathematics and the Associate Head of the Mathematics Department at the University of Georgia. There, he has won multiple awards for teaching, including the Lothar Tresp Outstandin g Honors Professor Award in 2002 and 2010, as well as the Honoratus Medal in 1992. Professor Shifrin was one of  five receipients of the University of Georgias 1997 Josiah Meigs Award for Excellence in Teaching, and in 2000 he was given the Southeastern MAA Award for Distinguished College or University Teaching of Mathematics. In addition to Linear Algebra: A Geometric Approach, Professor Shifrin has published the textbooks Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds and Abstract Algebra: A Geometric Approach, and he has also authored the Differential Geometry: A First Course in Curves and Surfaces, a free, online text that is widely used all over the world. His research interests and publications have focused on integral geometry and complex algebraic geometry.

Malcolm Adams

Malcolm Adams is a Professor of Mathematics and the Mathematics Department Head at the University of Georgia, where he also held the General Sandy Beaver Teaching Professorship from 2005-2008. He received is B.A. in Mathematics and Physics from the University of Oregon in 1978, and he earned his PhD in Mathematics from the Massachusetts Institute of Technology in 1982. Professor Adamss research interests focus on differential equations, especially in applications to biology and physics, and he has published another textbook, Measure Theory and Probability, with Victor Guillemin. Outside of the university, he enjoys running, traveling, and hiking with his wife and three children.