# How to evaluate the commutator of direct product?

1. May 31, 2012

### PRB147

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

2. May 31, 2012

### kith

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