The question is a bit vague, but here's my attempt at two different interpretations.
In the context of quantum physics, "quantised vectors" are not themselves quantised, it is the (usually energy) eigenvalue which is constrained to be specified values.
Just because you can multiply the eigenvectors by any scalar, doesn't mean all those scalars are meaningful.
In a mathematical sense, you can define a set of vectors on an integer lattice (quantised in the sense that in a basis aligned with the lattice all coordinates are integers), but then this is a vector space over the integers, such that the axiom you are talking about is only valid if the scalar is an integer.
almightyJack t1_iscggi6 wrote
Reply to How are quantized vectors vectors? by [deleted]
The question is a bit vague, but here's my attempt at two different interpretations.
In the context of quantum physics, "quantised vectors" are not themselves quantised, it is the (usually energy) eigenvalue which is constrained to be specified values.
Just because you can multiply the eigenvectors by any scalar, doesn't mean all those scalars are meaningful.
In a mathematical sense, you can define a set of vectors on an integer lattice (quantised in the sense that in a basis aligned with the lattice all coordinates are integers), but then this is a vector space over the integers, such that the axiom you are talking about is only valid if the scalar is an integer.