Some results on generalized Schur complements for the Kronecker product of positive semidefinite matrices

The generalized Schur complements for the Kronecker product of positive semidefinite matrices are studied with the properties of the Kronecker product and the permutation matrix.An identity of generalized Schur complements for the Kronecker product of positive semidefinite matrices is obtained,which extend the result to the generalized Schur complements of positive semidefinite matrices.Further,some inequalities are derived by properly changing the composition of γ'.