Necessary and Sufficient Conditions for the Existence of a Positive Definite Solution for the Matrix Equation | Zendy

Naglaa M. El–Shazly | Zendy

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Necessary and Sufficient Conditions for the Existence of a Positive Definite Solution for the Matrix Equation

Author(s) -

Naglaa M. El–Shazly

Publication year - 2013

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2013/537520

Subject(s) - invertible matrix , positive definite matrix , mathematics , integer (computer science) , matrix (chemical analysis) , identity matrix , pure mathematics , nonnegative matrix , integer matrix , mathematical analysis , symmetric matrix , physics , eigenvalues and eigenvectors , computer science , chemistry , quantum mechanics , chromatography , programming language

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

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