This question may seem similar to another one asked but it really isn't. We know that in physics for example, when we speak of space vectors, they are represented as arrows and these form a vector space. But there are other kinds of vector spaces for example, real valued functions on the unit interval [0,1]. The elements of these vector spaces typically cannot be visualized as arrows since that won't make sense for such elements so, we call them vectors if they satisfy the vector space axioms and that's that.
Can we also consider these vectors as having both magnitude and direction? I mean sure, if there is a norm on a vector space of functions, you can have magnitude but, I'm having trouble imagining directions being valid there. I looked far and wide for an answer and found none so any assistance is much appreciated.