I'm just learning about the whole Dirac notation stuff and I have come across the fact that bra's and ket's are somehow independent of bases. Or rather that they do not need the specification of a basis. I really don't understand this from a vector point of view. Maybe that is the problem, should I not be thinking about these like vectors? E.g. I understand that [itex]\mathbf e_i[/itex] needs a basis, but for some reason [itex]\mid e_i \rangle[/itex] doesn't? Thanks in advance!