Consider the quadratic matrix equation X T DX +AX +X T B + C = 0, where all the matrices are square and have the same order n. With this equation, a block matrix M of the double order 2n can be associated. The solvability of the equation turns out to be related to the existence of neutral subspaces of dimension n for M. The paper presents reasonably general conditions ensuring the existence of such subspaces.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 439, 2015, pp. 93–98.
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Ikramov, K.D. Neutral Subspaces of Complex Matrices. J Math Sci 216, 783–786 (2016). https://doi.org/10.1007/s10958-016-2942-7
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DOI: https://doi.org/10.1007/s10958-016-2942-7