Commutation theorem for traces

The commutation theorem for traces is a result in linear algebra and functional analysis, particularly within the context of operator theory. It deals with the properties of the trace operator, which is a map that takes a square matrix (or, more generally, a bounded operator on a Hilbert space) and sums its diagonal elements. The commutation theorem states that if two operators \( A \) and \( B \) commute (i.e.