In addition to the algebraic aspects of linear algebra presented earlier, there are many analytical and geometrical concepts which are usually included. This material involves the special fields ℝ and ℂ instead of general fields. It is these things which are typically generalized in functional analysis. The main new idea is that the notion of distance is included. This allows one to consider continuity, compactness, and many other topics from calculus. First is a general treatment of the notion of distance which has nothing to do with linear algebra but is a useful part of the vocabulary leading most efficiently to the inclusion of analytical topics.