Necessary and Sufficient Conditions for the Existence of a Hermitian Positive Definite Solution of a Type of Nonlinear Matrix Equations
2009 ◽
Vol 2009
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pp. 1-13
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Keyword(s):
We study the Hermitian positive definite solutions of the nonlinear matrix equationX+A∗X−2A=I, whereAis ann×nnonsingular matrix. Some necessary and sufficient conditions for the existence of a Hermitian positive definite solution of this equation are given. However, based on the necessary and sufficient conditions, some properties and the equivalent equations ofX+A∗X−2A=Iare presented while the matrix equation has a Hermitian positive definite solution.
2010 ◽
Vol 87
(11)
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pp. 2542-2551
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2011 ◽
Vol 2011
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pp. 1-18
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2017 ◽
Vol 52
(1)
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pp. 22-26
2014 ◽
Vol 2014
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pp. 1-8
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1993 ◽
Vol 186
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pp. 255-275
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2010 ◽
Vol 216
(12)
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pp. 3480-3485
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2017 ◽
Vol 18
(5)
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pp. 293-301