Handbook of Linear Algebra, 2nd Edition

Chapter 82

Geometry

Mark Hunacek

Iowa State University

Many topics taught in an introductory linear algebra course are often motivated by reference to elementary geometry. The geometry is treated as something the student is already familiar with, and reference to it is made to give the student a better understanding of algebraic concepts that may be considered, at least on first acquaintance, to be rather abstract. What is interesting and important is that the process can be reversed: Assuming the linear algebra as known, geometric concepts can be defined and developed on a rigorous basis. The use of vector methods in geometry often provides new ways of looking at old problems and also helps demonstrate deep and beautiful connections between ...