Optimization Of Some Hermitian Matrix Expressions And Its Applications To Statistics

In this paper, we derive some necessary and sufficient conditions for the existence of a solution to the system of mixed generalized Sylvester matrix equations where Ai,Bi,Cj,Dj,Ej,(i= 1,2,3, j= 1,2) are given complex matrices, X,Y,Z are variable matrices. We give an expression of the general solution to the above system when it is solvable. Moreover, we investigate the admissible ranks of the general solution to the system. As applications to statistics, we finally investigate Ordinary Least Square Estimation and its properties under the growth curle model with retriction.