Abstract
A generalized Sylvester matrix equation is considered. This equation is related with the stabilizer of a triple of matrices under the Lie group action on the space of triples of matrices which corresponds to the equivalence relation generalizing, in a natural way, the similarity between square matrices.criterion for the structural stability of a triple of matrices t is deduced in terms of therank of a matrix M(t). Also a differentiable family of triples of matrices is considered and we give conditions for differentiablity of the related family of tangent spaces to stabilizers T(ϕ(x)), deducing from it another criterion for structural stability of triples of matrices.
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