Solvability of the matrix inequality.

In this paper, we first investigate the matrix equation <inline-graphic></inline-graphic> in a new fashion, where A, B, C, D and G are arbitrary matrices. Then, we establish some necessary and sufficient conditions for the existence of a solution of <inline-graphic></inline-graphic>, where A, B are arbitrary matrices and C is a Hermitian matrix. In the special case when <inline-graphic></inline-graphic>, we determine the general solution of <inline-graphic></inline-graphic>, where A is an arbitrary matrix and C is a Hermitian matrix. [ABSTRACT FROM AUTHOR]