In general the tensor product $\varphi\otimes\psi$ is not commutative, but I was thinking that if I have tensor product on two orthonormal bases of Hilbert spaces are they commutative i.e is $$\varphi_i\otimes\varphi_j=\varphi_j\otimes\varphi_i$$ and if so why?
2026-03-27 11:46:08.1774611968
Is tensor product commutative on orthonormal basis?
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Since these are two vectors in a same natural basis (consisting of all $\varphi_i\otimes\varphi_j$) for the tensor product space, they are obviously distinct.