What are some disadvantages of using a basis whose elements are not orthogonal? (The set of vectors in a basis are linearly independent by definition.) One disadvantage is that for some vector $\vec v$, it involves more computation to find the coordinates with respect to a non-orthogonal basis. Are there any other undesirable outcomes?
I'm working on a simple model where it's more intuitive to use several physical but non-orthogonal entities as the basis.