Structural stability of pairs of matrices under contragredient equivalence
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A complex matrix pencil A-¿B is called structurally stable if there exists its neighborhood in which all pencils are strictly equivalent to this pencil. We describe all complex matrix pencils that are structurally stable. It is shown that there are no pairs (M,N) of m×n and n×m complex matrices (m,n=1) that are structurally stable under the contragredient equivalence (S-1MR,R-1NS), in which S and R are nonsingular.
CitationGarcia-Planas, M.I.; Klymchuk, T. Structural stability of pairs of matrices under contragredient equivalence. "Ukrainian Mathematical Journal", 2019, vol. 71, núm. 5, p. 706-709.