To “ Gemini : Graph Estimation with Matrix Variate Normal Instances

9. Notation and an outline. Suppose that we have n i.i.d. random matrices Xn = (X(1), X(2), . . . , X(n)) where X(i) ∼ Nf,m (0, A0 ⊗ B0) for all i, and A0 = (ajk) and B0 = (bjk) are positive definite. Let Y (t) = X(t) T , Ŝn = 1 n ∑n t=1 vec {X(t) } vec {X(t) } T , and S̃n = 1 n ∑n t=1 vec {Y(t) } vec {Y(t) } . Denote the `, kth block of size f × f in Ŝn by Ŝ`k n = (Ŝ`k ij ) and that of size m ×m in S̃n by S̃`k n = (S̃`k ij ). Let x(t)1, . . . , x(t)m ∈ R be column vectors and y(t)1, . . . , y(t)f ∈ Rm be row vectors of matrix X(t). Then