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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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/

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