Table of Contents

0. Motivation. 1. Vectors. 1.1. Vector Operations. 1.2. Span. 1.3. Linear Independence. 2. Functions of Vectors. 2.1. Linear Functions. 2.2. Matrices. 2.3. Matrix Operations. 2.4. Matrix Vector Spaces. 2.5. Kernel and Range. 2.6. Row Reduction. 2.7. Applications of Row Reduction. 2.8. Solution Sets. 2.9. Large Matrix Computations. 2.10. Invertibility. 2.11. The Invertible Matrix Theorem. 3. Vector Spaces. 3.1. Basis and Coordinates. 3.2. Polynomial Vector Spaces. 3.3. Other Vector Spaces. 4. Diagonalization. 4.1. Eigenvalues and Eigenvectors. 4.2. Determinants. 4.3. Eigenspaces. 4.4. Diagonalization. 4.5. Change of Basis Matrices. 5. Computational Vector Geometry. 5.1. Length. 5.2. Orthogonality. 5.3. Orthogonal Projection. 5.4. Orthogonal Basis. A. Appendices. A.1. Complex Numbers. A.2. Mathematica. A.3. Solutions to Odd Exercises. Bibliography. Index.

About the Author

Dr. Hannah Robbins is an associate professor of Mathematics at Roanoke College in Salem Virginia. Formerly a commutative algebraist, she now studies applications of linear algebra and assesses teaching practices in calculus. Outside the office she enjoys hiking and playing bluegrass bass.