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

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  • Naglaa M. El-Shazly

Abstract

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.

Suggested Citation

  • Naglaa M. El-Shazly, 2013. "Necessary and Sufficient Conditions for the Existence of a Positive Definite Solution for the Matrix Equation," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, June.
  • Handle: RePEc:hin:jnljam:537520
    DOI: 10.1155/2013/537520
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