Abstract
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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Ikramov, K.D. On a Remarkable Property of a Matrix of Mark Kac. Mathematical Notes 72, 325–330 (2002). https://doi.org/10.1023/A:1020543219652
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DOI: https://doi.org/10.1023/A:1020543219652