Geodesic
On a Remarkable Property of a Matrix of Mark Kac
Matematičeskie zametki, Tome 72 (2002) no. 3, pp. 356-362

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A triangular submatrix extracted in a special way from the Mark Kac matrix has a remarkable spectral property: if the order of its columns is reversed, then half of the eigenvalues do not change, whereas the other half are multiplied by -1. This fact discovered by this author somewhat earlier has had no explanation until now. Such an explanation is given in this paper. 
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     title = {On a {Remarkable} {Property} of a {Matrix} of {Mark} {Kac}},
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Kh. D. Ikramov. On a Remarkable Property of a Matrix of Mark Kac. Matematičeskie zametki, Tome 72 (2002) no. 3, pp. 356-362. http://geodesic.mathdoc.fr/item/MZM_2002_72_3_a3/