Chapter 1. Vectors and Matrices.- Chapter 2.  Matrix Algebra.- Chapter 3. Vector Spaces.- Chapter 4. Projections and Linear Transformations.- Chapter 5. Determinants.- Chapter 6. Eigenvalues and Eigenvectors.- 

Linear Algebra: A Geometric Approach, Second Edition, is a text that not only presents the standard computational aspects of linear algebra and interesting applications, it guides students to think about mathematical concepts and write rigorous mathematical arguments. This thought-provoking introduction to the subject and its myriad applications is interesting to the science or engineering student but will also help the mathematics student make the transition to more abstract advanced courses. The second edition has been updated with additional examples and exercises and has been streamlined for easier teaching and studying.

Geometry is introduced early, using vector algebra to do analytic geometry in the first section and dot product in the second.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.New_to_this_editionAn extra 20% more exercises have been added throughout the text to reinforce key concepts and give students practice in computation.A stronger emphasis has been placed throughout on key concepts and understanding, through new proofs and a variety of text exercises.Additional material has been included, such as coverage of vectors and matrices in chapter 1 and matrix algebra in chapter 2.