In this paper it is shown that if T is a compact linear map of a Hilbert space to itself and \(| T|\) is the positive square root of \(T^*T\), then for all \(n\in {\mathbb{N}}\), \(e_ n(T)=e_ n(T^*)=e_ n(| T|)\), where \(e_ n(S)\) is the \(n^{th}\) entropy number of S.