Geodesic
On the Matrix Equation $X^{-1}X^*=A$
Matematičeskie zametki, Tome 71 (2002) no. 4, pp. 548-553

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Solvability conditions are examined for the matrix equation $$ X^{-1}X^*=A, $$ which cannot be found in the well-known reference books on matrix theory. Methods for constructing solutions to this equation are indicated. 
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     author = {Kh. D. Ikramov},
     title = {On the {Matrix} {Equation} $X^{-1}X^*=A$},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
     volume = {71},
     number = {4},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_4_a5/}
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Kh. D. Ikramov. On the Matrix Equation $X^{-1}X^*=A$. Matematičeskie zametki, Tome 71 (2002) no. 4, pp. 548-553. http://geodesic.mathdoc.fr/item/MZM_2002_71_4_a5/