I'm trying to rehearse a course I took long ago in linear algebra in light of what I've studies in economy classes lately. Specifically, I want to know how the concepts of basis, and angles between vectors and orthogonality relates to non-geometric vectors such as economic data.
Let's say I'm dealing with time series of economic data, and I want to do regression analysis of a certain variable (let's say a stock index) on other variables (let's say lags of itself and GDP) and I represent my information by column vectors.
1. Is there such a concept as angles between such vectors? If so, what does that really mean, conceptually?
2. What would the basis typically be in such a case? Is it always orthonormal since we're dealing with non-geometric entities (therefore orthogonal) who's quantities are measured as multiples of a certain unit measurement (a dollar perhaps) (thus normalized)?
I'm sorry if this seems confused, but I'm learning alone at the moment so... ;-)