### RANKS OF SUBMATRICES IN THE REFLEXIVE SOLUTIONS OF SOME MATRIX EQUATIONS

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#### Abstract

Maximal and minimal ranks of the two submatrices X₁ and X₂ in the (skew-) Hermitian reflexive solution X=U[

X₁ 0

0 X₂

]U^{∗} of the matrix equation AXA^{∗}=C, in the reflexive solution of the matrix equation AXB=C are derived. Then necessary and sufficient conditions for these reflexive solutions to have special forms, and the general expressions of these reflexive solutions are achieved.

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DOI: https://doi.org/10.22190/FUMI220922003G

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