  Here, a Separation Theorem about K-Independent Subspace Analysis (K real or
complex), a generalization of K-Independent Component Analysis (KICA) is
proven. According to the theorem, KISA estimation can be executed in two steps
under certain conditions. In the first step, 1-dimensional KICA estimation is
executed. In the second step, optimal permutation of the KICA elements is
searched for. We present sufficient conditions for the KISA Separation Theorem.
Namely, we shall show that (i) spherically symmetric sources (both for real and
complex cases), as well as (ii) real 2-dimensional sources invariant to 90
degree rotation, among others, satisfy the conditions of the theorem.
