Necessary and sufficient conditions for the existence of positive definite solutions of the matrix equation X + A T X -2 A = I

Author: Ramadan Mohamed  

Publisher: Taylor & Francis Ltd

ISSN: 0020-7160

Source: International Journal of Computer Mathematics, Vol.82, Iss.7, 2005-07, pp. : 865-870

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Abstract

Necessary and sufficient conditions for the matrix equation X + A T X -2 A = I to have a real symmetric positive definite solution X are derived. Based on these conditions, some properties of the matrix A as well as relations between the solution X and A are derived.