Necessary and Sufficient Conditions for the Existence of a Positive Definite Solution for the Matrix Equation
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 , . Mo...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/537520 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832567049827647488 |
|---|---|
| author | Naglaa M. El-Shazly |
| author_facet | Naglaa M. El-Shazly |
| author_sort | Naglaa M. El-Shazly |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a9a6a910853043808cc2327a7e8611ab |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-a9a6a910853043808cc2327a7e8611ab2025-02-03T01:02:26ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/537520537520Necessary and Sufficient Conditions for the Existence of a Positive Definite Solution for the Matrix EquationNaglaa M. El-Shazly0Department of Mathematics, Faculty of Science, Menoufia University, Shebin El-Koom, EgyptIn 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.http://dx.doi.org/10.1155/2013/537520 |
| spellingShingle | Naglaa M. El-Shazly Necessary and Sufficient Conditions for the Existence of a Positive Definite Solution for the Matrix Equation Journal of Applied Mathematics |
| title | Necessary and Sufficient Conditions for the Existence of a
Positive Definite Solution for the Matrix Equation |
| title_full | Necessary and Sufficient Conditions for the Existence of a
Positive Definite Solution for the Matrix Equation |
| title_fullStr | Necessary and Sufficient Conditions for the Existence of a
Positive Definite Solution for the Matrix Equation |
| title_full_unstemmed | Necessary and Sufficient Conditions for the Existence of a
Positive Definite Solution for the Matrix Equation |
| title_short | Necessary and Sufficient Conditions for the Existence of a
Positive Definite Solution for the Matrix Equation |
| title_sort | necessary and sufficient conditions for the existence of a positive definite solution for the matrix equation |
| url | http://dx.doi.org/10.1155/2013/537520 |
| work_keys_str_mv | AT naglaamelshazly necessaryandsufficientconditionsfortheexistenceofapositivedefinitesolutionforthematrixequation |