Linear Algebra via Exterior Products

This is a pedagogical introduction to the coordinate-free approach in basic finite-dimensional linear algebra. The reader should be already exposed to the array-based formalism of vector and matrix calculations. This book makes extensive use of the exterior (anti-commutative wedge) product of vectors. The coordinate-free formalism and the exterior product while somewhat more abstract provide a deeper understanding of the classical results in linear algebra. Without cumbersome matrix calculations this text derives the standard properties of determinants the Pythagorean formula for multidimensional volumes the formulas of Jacobi and Liouville the Cayley-Hamilton theorem the Jordan canonical form the properties of Pfaffians as well as some generalizations of these results.