@article{Chen2026, 
author = {Yinlan Chen and Qingyi Yang and Honglin Zou},
title = {Symmetric nonnegative definite solutions of certain linear matrix equations on a subspace},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {21727-21742},
keywords = {subspace, nonnegative matrix, generalized inverse, orthogonal projector},
url = {https://www.sciopen.com/article/10.3934/math.2026879},
doi = {10.3934/math.2026879},
abstract = {For a given matrix    G  ∈            R              l      ×      n      , define a subspace    Ω by    Ω  =      {          z      ∈                        R                n            ∣      G      z      =      0        }  , and let        H    =      {          K      ∈                        R                          n          ×          n                    ∣      (      x      ,      K      y      )      =      (      K      x      ,      y      )      ,                    x        ⊤            K      x      ≥      0      ,            ∀      x      ,      y      ∈      Ω        }  . Thus,        H   consists of all symmetric nonnegative definite matrices on the subspace    Ω. In this paper, we investigate the existence of    X  ∈      H   satisfying the linear matrix equations    A  X  =  C  ,  X  B  =  D, and    A  X  B  =  D. A necessary and sufficient condition for solvability and an explicit representation of the general solution are obtained. Finally, two numerical examples are provided to demonstrate the accuracy of the results.}
}