Geodesic
Non-Hermitian Matrices of Even Order and Neutral Subspaces of Half the Dimension
Matematičeskie zametki, Tome 100 (2016) no. 5, pp. 739-743.

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Consider the sesquilinear matrix equation $X^*DX+AX+X^*B+C=0$, where all the matrices are square and have the same order $n$. With this equation, we associate a block matrix $M$ of double order $2n$. The solvability of the above equation turns out to be related to the existence of $n$-dimensional neutral subspaces for the matrix $M$. We indicate sufficiently general conditions ensuring the existence of such subspaces.
Keywords: sesquilinear matrix equation, neutral subspace, congruence, cosquare
Mots-clés : Jordan form. 
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Kh. D. Ikramov. Non-Hermitian Matrices of Even Order and Neutral Subspaces of Half the Dimension. Matematičeskie zametki, Tome 100 (2016) no. 5, pp. 739-743. http://geodesic.mathdoc.fr/item/MZM_2016_100_5_a8/

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