Since the term − − 1 2 T r ρ ρ K K ∗ ∗ is concave (it is linear), the conjecture reduces to the problem of concavity of T r ρ ρ p K ∗ ∗ ρ ρ 1 − − p K . As noted in, this conjecture (for all 0 ≤ ≤ p ≤ ≤ 1 ) implies SSA, and was proved for p = 1 2 in, and for all 0 ≤ ≤ p ≤ ≤ 1 in in the following more general form: The function of two matrix variables