how to evaluate the commutator of direct product?

PRB147

assuming that A B C D are all [tex]n\times n [/tex] operators
how to evaluate the commutator of direct product?
[tex][A\otimes B, C\otimes D][/tex]

kith

[itex][A\otimes B, C\otimes D][/itex] is defined as [itex]A\otimes B \cdot C\otimes D - C\otimes D \cdot A\otimes B[/itex] which is [itex]AC\otimes BD - CA\otimes DB[/itex].

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PRB147	how to evaluate the commutator of direct product? Tweet assuming that A B C D are all [tex]n\times n [/tex] operators how to evaluate the commutator of direct product? [tex][A\otimes B, C\otimes D][/tex]

kith	[itex][A\otimes B, C\otimes D][/itex] is defined as [itex]A\otimes B \cdot C\otimes D - C\otimes D \cdot A\otimes B[/itex] which is [itex]AC\otimes BD - CA\otimes DB[/itex].