Solvability conditions for the matrix equation $X^{\mathrm{T}}DX+AX+X^{\mathrm{T}}B+C=0$
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 4, pp. 555-557 Cet article a éte moissonné depuis la source Math-Net.Ru

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Under certain restrictions on the matrix coefficients of the quadratic matrix equation $X^{\mathrm{T}}DX+AX+X^{\mathrm{T}}B+C=0$, solvability conditions for this equation are given, and its relationship with an equation of the form $XAX=B$ is found. Certain specific types of matrix coefficients obeying the above solvability conditions are indicated.
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Yu. O. Vorontsov. Solvability conditions for the matrix equation $X^{\mathrm{T}}DX+AX+X^{\mathrm{T}}B+C=0$. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 4, pp. 555-557. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_4_a2/

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[2] Ikramov X. D., “O razreshimosti odnogo klassa kvadratichnykh matrichnykh uravnenii”, Dokl. AN, 455:2 (2014), 135–137 | Zbl