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

Linear Algebra

Second Edition  ©2011 Ted Shifrin; Malcolm Adams Formats: E-book

Authors

  • Headshot of Ted Shifrin

    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.

  • Headshot of Malcolm Adams

    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.

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

Product Updates

Master Linear Algebra with Greater Clarity and Precision

Originally published in 2010, this text returns in a fully revised edition designed to deepen conceptual understanding and sharpen problem-solving skills. This updated edition retains the core strengths instructors have relied on while adding expanded practice, refined explanations, and key structural enhancements to guide students through the rigor of linear algebra.

What's Updated in This Edition
  • 20% more exercises have been added throughout the text to reinforce core concepts and provide extensive computational practice.
  • A stronger focus on rigor brings additional proofs and a wider range of fresh text exercises, deepening students' engagement with foundational ideas.
  • Integrated guidance boxes, distributed across chapters, walk students through logic, proof techniques, and strategic problem-solving tips to support their transition into abstract mathematical thinking.
Chapter Highlights
  • Chapter 1: Vectors and Matrices now includes fresh proof reasoning examples.
  • Chapter 2: Matrix Algebra features new sections on Linear Transformations and Elementary Matrices.
  • Chapter 3: Vector Spaces offers a streamlined treatment of the four fundamental subspaces alongside clarified coverage of linear independence and bases.
  • Chapters 4 & 5: Projections, Linear Transformations, and Determinants have been reorganized and updated for clearer explanations of Change of Basis and geometric concepts.

Authors

  • Headshot of Ted Shifrin

    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.

  • Headshot of Malcolm Adams

    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.

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

Product Updates

Master Linear Algebra with Greater Clarity and Precision

Originally published in 2010, this text returns in a fully revised edition designed to deepen conceptual understanding and sharpen problem-solving skills. This updated edition retains the core strengths instructors have relied on while adding expanded practice, refined explanations, and key structural enhancements to guide students through the rigor of linear algebra.

What's Updated in This Edition
  • 20% more exercises have been added throughout the text to reinforce core concepts and provide extensive computational practice.
  • A stronger focus on rigor brings additional proofs and a wider range of fresh text exercises, deepening students' engagement with foundational ideas.
  • Integrated guidance boxes, distributed across chapters, walk students through logic, proof techniques, and strategic problem-solving tips to support their transition into abstract mathematical thinking.
Chapter Highlights
  • Chapter 1: Vectors and Matrices now includes fresh proof reasoning examples.
  • Chapter 2: Matrix Algebra features new sections on Linear Transformations and Elementary Matrices.
  • Chapter 3: Vector Spaces offers a streamlined treatment of the four fundamental subspaces alongside clarified coverage of linear independence and bases.
  • Chapters 4 & 5: Projections, Linear Transformations, and Determinants have been reorganized and updated for clearer explanations of Change of Basis and geometric concepts.

Now available as an accessible ebook!

Linear Algebra: A Geometric Approach, Second Edition, presents the standard computational aspects of linear algebra through a geometric approach, giving instructors a text that builds technical skill alongside mathematical maturity.

  • A range of intriguing applications helps motivate science and engineering students by connecting the math to problems they'll encounter in their fields.
  • Support for the transition to abstract coursework helps mathematics students move from computational linear algebra into more advanced, abstract courses.
  • Guidance on mathematical thinking and writing teaches students how to reason through mathematical concepts and construct rigorous mathematical arguments.

ISBN:9781319658618

If you can't find what you are looking for contact your sales rep.