For the first time, a manifold of symmetric real matrices with fixed multiplicities of eigenvalues was considered by Arnold. In the case of compact real self-adjoint operators, similar results were obtained by Japanese mathematicians Fujiwara, Tanikawa, and Yukita. They introduced a special local diffeomorphism “straightening” the Arnold manifold. Later, the properties of the indicated diffeomorphism were studied by Dymarskii. We describe the smooth structure of submanifolds of finite-dimensional and compact operators of the general form in which a selected eigenvalue is associated with a single Jordan block.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 9, pp. 1179–1189, September, 2011.
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Bondar’, A.A., Dymarskii, Y.M. Submanifolds of compact operators with fixed multiplicities of eigenvalues. Ukr Math J 63, 1349–1360 (2012). https://doi.org/10.1007/s11253-012-0583-7
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DOI: https://doi.org/10.1007/s11253-012-0583-7