I would like to declare spin states; spin up (alpha) and spin down (beta)

such that they form an orthogonal basis not necessarily using Dirac Ket notaion.  I am using the Physics package and Linear Algebra

When I try to use the Dirac Ket notation, I have noncommuting issues with the Cartesian basis

Cart := Vector[column](3, [Ket(X), Ket(Y), Ket(Z)]);

Spin := Vector[column](2, [Ket(alpha), Ket(beta)]);