The sources and application fields of nonlinear matrix equations are quite extensive, including control theory, statistics, dynamic programming, etc. A large number of problems can be transformed into solving matrix equations. In this paper we establish some necessary and sufficient conditions for the existence of positive definite solutions to the nonlinear matrix equation ATXA = ηX. The existence of positive definite solutions to corresponding inequalities were discussed too. In addition, some examples are presented to illustrate the main results of this paper.
| Published in | Innovation (Volume 4, Issue 2) |
| DOI | 10.11648/j.innov.20230402.12 |
| Page(s) | 25-28 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2023. Published by Science Publishing Group |
Positive Definite Solution, Matrix Equations, Nonlinear Equations
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APA Style
Yang, R. (2023). Positive Definite Solution of a Class of Matrix Equations. Innovation, 4(2), 25-28. https://doi.org/10.11648/j.innov.20230402.12
ACS Style
Yang, R. Positive Definite Solution of a Class of Matrix Equations. Innovation. 2023, 4(2), 25-28. doi: 10.11648/j.innov.20230402.12
AMA Style
Yang R. Positive Definite Solution of a Class of Matrix Equations. Innovation. 2023;4(2):25-28. doi: 10.11648/j.innov.20230402.12
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Download@article{10.11648/j.innov.20230402.12,
author = {Ran Yang},
title = {Positive Definite Solution of a Class of Matrix Equations},
journal = {Innovation},
volume = {4},
number = {2},
pages = {25-28},
doi = {10.11648/j.innov.20230402.12},
url = {https://doi.org/10.11648/j.innov.20230402.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.innov.20230402.12},
abstract = {The sources and application fields of nonlinear matrix equations are quite extensive, including control theory, statistics, dynamic programming, etc. A large number of problems can be transformed into solving matrix equations. In this paper we establish some necessary and sufficient conditions for the existence of positive definite solutions to the nonlinear matrix equation ATXA = ηX. The existence of positive definite solutions to corresponding inequalities were discussed too. In addition, some examples are presented to illustrate the main results of this paper.
},
year = {2023}
}
TY - JOUR T1 - Positive Definite Solution of a Class of Matrix Equations AU - Ran Yang Y1 - 2023/12/05 PY - 2023 N1 - https://doi.org/10.11648/j.innov.20230402.12 DO - 10.11648/j.innov.20230402.12 T2 - Innovation JF - Innovation JO - Innovation SP - 25 EP - 28 PB - Science Publishing Group SN - 2994-7138 UR - https://doi.org/10.11648/j.innov.20230402.12 AB - The sources and application fields of nonlinear matrix equations are quite extensive, including control theory, statistics, dynamic programming, etc. A large number of problems can be transformed into solving matrix equations. In this paper we establish some necessary and sufficient conditions for the existence of positive definite solutions to the nonlinear matrix equation ATXA = ηX. The existence of positive definite solutions to corresponding inequalities were discussed too. In addition, some examples are presented to illustrate the main results of this paper. VL - 4 IS - 2 ER -
School of Mathematics and Statistics, Shandong Normal University, Jinan, P. R. China
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