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I know how to interpret a vector, inner product etcetera in one Hilbert space. However, I can not get my head around how the direct product of two (or more) Hilbert spaces can be interpreted.

For instance, the Hilbert space ##W## of a larger system is spanned by the direct product of the Hilbert spaces of the subsystem, ## W = A \otimes B##. If the states ##| n_A\rangle## denote the basis states in ##A## and ##|m_B\rangle## those in ##B##, then any state in ##W## can be written as ##|\psi_W\rangle = \sum_{n,m} c_{nm}|n_A\rangle \otimes |m_B\rangle##.

How do you interpret the direct product of two Hilbert spaces?

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# I Interpretation of direct product of Hilbert spaces

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