Abstract
Consider the sesquilinearmatrix 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.
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Kh. D. Ikramov, “On the solvability of a certain class of sesquilinear matrix equations,” Dokl. Ross. Akad. Nauk 454 (3), 265–267 (2014) [Dokl. Math. 89 (1), 57–58 (2014)].
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Original Russian Text © Kh. D. Ikramov, 2016, published in Matematicheskie Zametki, 2016, Vol. 100, No. 5, pp. 739–743.
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Ikramov, K.D. Non-Hermitian matrices of even order and neutral subspaces of half the dimension. Math Notes 100, 720–723 (2016). https://doi.org/10.1134/S0001434616110080
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DOI: https://doi.org/10.1134/S0001434616110080