Necessary and Sufficient Conditions for the Existence of a Positive Definite Solution for the Matrix Equation - Naglaa M. El-Shazly (Journal of Applied Mathematics)
In this paper necessary and sufficient conditions for the matrix equation to have a positive definite solution are derived, where , is an identity matrix, are nonsingular real matrices, and is an odd positive integer. These conditions are used to propose some properties on the matrices , . Moreover, relations between the solution and the matrices are derived.