Elsevier

Linear Algebra and its Applications

Volume 194, 15 November 1993, Pages 91-108
Linear Algebra and its Applications

On the existence of a positive definite solution of the matrix equation X+ATX−1A= I

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Abstract

The question is raised under which conditions on the real (square) matrix A the matrix equation X+ATX−1A=I has a real symmetric positive definite solution X. Both necessary and sufficient solvability conditions on A are derived. Moreover, we give an algorithm to calculate the solution. For a number of special cases we also present an analytic solution.

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