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Miniversal deformations of chains of linear mappings
T. N. Gaiduk, V. V. Sergeichuk, N. A. Zharko
V.I. Arnold [Russian Math. Surveys, 26 (no. 2), 1971, pp. 29-43] gave a miniversal deformation of matrices of linear operators; that is, a simple canonical form, to which not only…
Rigid systems of second-order linear differential equations
M. Isabel Garcia-Planas, M. Dolors Magret, Vladimir V. Sergeichuk +1
We say that a system of differential equations d^2x(t)/dt^2=Adx(t)/dt+Bx(t)+Cu(t), in which A and B are m-by-m complex matrices and C is an m-by-n complex matrix, is rigid if it ca…
Positivity criteria generalizing the leading principal minors criterion
Vyacheslav Futorny, Vladimir V. Sergeichuk, Nadya Zharko
For each Hermitian matrix, we prove that instead of the leading principal minors some of their sums can be used in the leading principal minors criterion and in other inertia probl…