@article{Chen2022, 
author = {Yinlan Chen and Lina Liu},
title = {The common Re-nonnegative definite and Re-positive definite solutions to the matrix equations        A    1    X      A    1    ∗    =      C    1   and        A    2    X      A    2    ∗    =      C    2},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {1},
pages = {384-397},
keywords = {matrix equation, Re-nonnegative definite solution, Re-positive definite solution, Moore-Penrose inverse, generalized singular value decomposition},
url = {https://www.sciopen.com/article/10.3934/math.2022026},
doi = {10.3934/math.2022026},
abstract = {In this paper, we consider the common Re-nonnegative definite (Re-nnd) and Re-positive definite (Re-pd) solutions to a pair of linear matrix equations        A    1    X      A    1    ∗    =      C    1    ,        A    2    X      A    2    ∗    =      C    2   and present some necessary and sufficient conditions for their solvability as well as the explicit expressions for the general common Re-nnd and Re-pd solutions when the consistent conditions are satisfied.}
}