Before I start asking the question, I want to apologize for my illiteracy in latex maths and the abstraction of my question.
My question is, is it possible for me to define a hypothetical 4 dimensional vector space? For example, if I defined a b c and d as my four unit vectors, can I create an orthogonal vector space where they are all orthogonal to each other. It is not possible spatially I can understand because spatial cartesian system is limited to 3 unit vectors and the 4th must be a linear combination of the other 3, but is it mathematically possible to have an orthogonal vector space in 4 dimensions?? I don't want to visualize it, but does mathematics allow for it? And how will my vector products of my space be defined in that situation? I understand that my inner products of my unit vectors with each other will be zero.