I'm going to plug Alan Macdonald's Linear and Geometric Algebra book as a great way to get an intuitive grip on the latter parts of this blog post
this is just a collection of basic facts and definitions with bad language. for example, inner product space is the correct nomenclature. euclidean space refers to an inner product space with the euclidean norm, i.e., the dot product. euclidean space should not be used to refer to a general inner product space.
This particular topic is something that all 19 year old electrical/mechatronic engineering students at my university in Australia learn, so it's probably a standard topic around the world (I think it's used to understand Fourier analysis in more advanced courses). Currently the post reads similar to what most readers would have encountered over the course of a 2 hour lecture, so my advice would be to vary the tone so that it's more conversational, giving you the opportunity to add your own insight to the problem.<p>The problem is that you need to have mulled over the problem for months to years before you can develop insight.