Geodesic
On the Matrix Equation $X^{-1}X^*=A$
Matematičeskie zametki, Tome 71 (2002) no. 4, pp. 548-553 
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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     author = {Kh. D. Ikramov},
     title = {On the {Matrix} {Equation} $X^{-1}X^*=A$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {548--553},
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     volume = {71},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2002_71_4_a5/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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[2] Lankaster P., Teoriya matrits, Nauka, M., 1978

[3] Khorn R., Dzhonson Ch., Matrichnyi analiz, Mir, M., 1990

[4] Ikramov Kh. D., Zadachnik po lineinoi algebre, Nauka, M., 1975

[5] Maltsev A. I., Osnovy lineinoi algebry, Nauka, M., 1970 | Zbl

[6] Gohberg I., Lancaster P., Rodman L., Matrices and Indefinite Scalar Products, Birkhäuser-Verlag, Boston, 1983

[7] Ikramov Kh. D., Chislennoe reshenie matrichnykh uravnenii, Nauka, M., 1984 | Zbl