Geodesic
Neutral subspaces of complex matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVIII, Tome 439 (2015), pp. 93-98

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Consider the quadratic matrix equation $X^TDX+AX+X^TB+C=0$, where all the matrices are square and have the same order $n$. With this equation, we associate a block matrix $M$ of the double order $2n$. the solvability of the equation turns out to be related to the existence of neutral subspaces of dimension $n$ for this matrix. Reasonably general conditions ensuring the existence of such subspaces are presented. 
@article{ZNSL_2015_439_a7,
     author = {Kh. D. Ikramov},
     title = {Neutral subspaces of complex matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {93--98},
     publisher = {mathdoc},
     volume = {439},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_439_a7/}
}
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Kh. D. Ikramov. Neutral subspaces of complex matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVIII, Tome 439 (2015), pp. 93-98. http://geodesic.mathdoc.fr/item/ZNSL_2015_439_a7/