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International Journal of Computer Mathematics Volume 82, 2005 - Issue 7
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Original Articles

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

Mohamed A. Ramadan Department of Mathematics, Faculty of Science, Menoufia University, EgyptCorrespondence[email protected]
Pages 865-870 | Received 23 Apr 2004, Published online: 25 Jan 2007
 
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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.

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