Geodesic
The structure of solutions of the matrix equation $J_n(0) Y + Y^{\mathsf{T}} J_n(0) = 0$ for even $n$
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIII, Tome 496 (2020), pp. 97-100

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It is shown that every solution of the matrix equation in the title of the paper, where $n = 2m$, can be transformed by a symmetric permutation of rows and columns to the direct sum of two triangular Toeplitz matrices of order $m$. 
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     author = {Kh. D. Ikramov},
     title = {The structure of solutions of the matrix equation $J_n(0) Y + Y^{\mathsf{T}} J_n(0) = 0$ for even $n$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {97--100},
     publisher = {mathdoc},
     volume = {496},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_496_a6/}
}
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Kh. D. Ikramov. The structure of solutions of the matrix equation $J_n(0) Y + Y^{\mathsf{T}} J_n(0) = 0$ for even $n$. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIII, Tome 496 (2020), pp. 97-100. http://geodesic.mathdoc.fr/item/ZNSL_2020_496_a6/