x1 is a vector (mathematical object/number/operator) representing or meaning (object/information) x2 with properties x3
This definition refers to the object, not the representation. A given vektori is not changed by a change of basis no matter how its appearance does, and two vektori may not be the same even if they are represented in equivalent forms in some bases (or even the same one). The object need only satisfy the vector axioms. A vector is not really a list. Since this word does not really concern itself with dual spaces, its scope probably includes many bras and/or kets (although the context/meaning of the bra/ket matters). It is possible, when x2 is not explicitly filled, for the vektori to have no meaning - it might just be a mathematical object with no further content.