- Home
- Mathematics
- Linear Algebra
Linear Algebra
A Geometric ApproachSecond Edition| ©2011 Ted Shifrin; Malcolm Adams
ISBN:9781429215213
Read and study old-school with our bound texts.
![Cover: Linear Algebra, 2nd Edition by Ted Shifrin; Malcolm Adams](http://prod-cat-files.macmillan.cloud/MediaResources/Jackets/258W/9781429215213.jpg)
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.
Features
Concepts and understanding is emphasized, doing proofs in text and providing plenty of exercises. To aid the student in adjusting to the mathematical rigor, blue boxes are provided which discuss matters of logic and proof technique or advice on formulating problem-solving strategies.
Rotations, reflections, and projections are used as a first brush with the notion of linear transformation when introducing matrix multiplication. Linear transformations are then treated in concert with the discussion of projections. Thus, the change-of-basis formula is motivated by starting with a coordinate system in which a geometrically defined linear transformation is clearly understood and asking for its standard matrix.
Orthogonal complements are emphasized, with their role in finding a homogenous system of linear equations that defines a given subspace of Rn.
New to This Edition
New Blue Boxes, integrated throughout the text, discuss matters of logic and proof techniques or advice on formulating problem-solving strategies to aid the student in adjusting to the mathematical rigor.
![Cover: Linear Algebra, 2nd Edition by Ted Shifrin; Malcolm Adams](http://prod-cat-files.macmillan.cloud/MediaResources/Jackets/258W/9781429215213.jpg)
Linear Algebra
Second Edition| ©2011
Ted Shifrin; Malcolm Adams
Digital Options
![Cover: Linear Algebra, 2nd Edition by Ted Shifrin; Malcolm Adams](http://prod-cat-files.macmillan.cloud/MediaResources/Jackets/258W/9781429215213.jpg)
Linear Algebra
Second Edition| 2011
Ted Shifrin; Malcolm Adams
Table of Contents
Foreword to the Instructor
Foreword to the Student
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
1. Matrix Operations
2. Linear Transformations: An Introduction
3. Inverse Matrices
4. Elementary Matrices: Rows get Equal Time
5. The Transpose
1. Subspaces of Rn
3. Linear Independence and Basis
4. Dimension and Its Consequences
5. A Graphic Example
6. Abstract Vector Spaces
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
1. Properties of Determinants
2. Cofactors and Cramer’s Rule
3. Signed Area in R2 and Signed Volume in R2
1. The Characteristic Polynomial
2. Diagonalizability
3. Applications
4. The Spectral Theorem
1. Complex Eigenvalues and Jordan Canonical Form
2. Computer Graphics and Geometry
3. Matrix Exponentials and Differential Equations
Answers to Selected Exercises
List of Blue Boxes
Index
Authors
![Headshot of Ted Shifrin](http://prod-cat-files.macmillan.cloud/MediaResources/Authors/207W/4730.jpg)
Ted Shifrin
![Headshot of Malcolm Adams](http://prod-cat-files.macmillan.cloud/MediaResources/Authors/207W/4468.jpg)
Malcolm Adams
![Cover: Linear Algebra, 2nd Edition by Ted Shifrin; Malcolm Adams](http://prod-cat-files.macmillan.cloud/MediaResources/Jackets/258W/9781429215213.jpg)
Linear Algebra
Second Edition| 2011
Ted Shifrin; Malcolm Adams
Related Titles
Select a demo to view:
![Achieve icon](http://prod-cat-files.macmillan.cloud/MediaResources/instructorcatalog/college/digital/digital-icons/PNG/digital-icon-achieve.png)
![](/college/_ui/responsive/common/images/spinner.gif)