Before revision: For general complex or real 1-parameter matrix flow A(t)_{n,n} \CC this paper considers ways to decompose flows globally via one constant matrix  C_{n,n} as A(t) = C ^{-1} \cdot diag(A_1(t), ..., A_\ell(t)) \cdot C \cdot diag(A_1,...,A_\ell)\cdot C } with each diagonal blockA _k(t) square and the number of blocks \ell > 1 if  possible.
After revision: For general complex or real 1-parameter matrix flow A(t)_{n,n} \CC this paper considers ways to decompose flows globally via one constant matrix similarity C_{n,n} as A(t) = C ^{-1} \cdot diag(A_1(t), ..., A_\ell(t)) \cdot C \cdot diag(A_1,...,A_\ell)\cdot C } with each diagonal blockA _k(t) square and the number of blocks \ell > 1 if possible.