Beyond what the axioms decribe as a vector space, what is a vector space?
Generally a vector space is a mathematical concept. A “vector” is simply a collection of some kind of conceptual objects that have some sort of zero defined and some way of defining addition, subtraction, negative, and multiplication by a scalar. You can have a vector of matrices, with each element in the vector being a matrix, or you can have a vector of purple fuzzy people, as long as you can define zero, addition, and scalar multiplication of purple fuzzy people. A vector space is essentially a collection of all vectors of a certain type that meet certain criteria. For example, you can have a vector space of purple fuzzy people, of vectors of 3 purple fuzzy people (3 fuzzy dimensions) each, and consisting only of purple fuzzy people with a blue spot on their heads if you can define mathematically the way they have a blue spot on their head and the definition allows for the vector space axioms to hold.
