RANKS OF SUBMATRICES IN THE REFLEXIVE SOLUTIONS OF SOME MATRIX EQUATIONS
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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