i never took functional analysis, but is orthogonal strictly required in a function space? in finite dim vector spaces, you don't need orthogonal to have a comp

i never took functional analysis, but is orthogonal strictly required in a function space? in finite dim vector spaces, you don't need orthogonal to have a complete basis, it is just cleaner. You only need linear independence. (1,2), (0,1) is just as much a basis set of R^2 as (0,1) (1,0)