A generalized sylvester equation: a criterion for structural staility of triples of matrices

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 matri...

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Published inLinear & multilinear algebra Vol. 44; no. 2; pp. 93 - 109
Main Authors Isabel Garciá-Planas, Ma, Dolors Magret, Ma
Format Journal Article
LanguageEnglish
Published Gordon and Breach Science Publishers 01.07.1998
Subjects
AMS Subject Classification: 15A21
stabilizer; continuous/differentiable family
Structural stability
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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.
AbstractList 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.
Author Dolors Magret, Ma
Isabel Garciá-Planas, Ma
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Cites_doi 10.1016/0024-3795(94)90352-2
10.1016/0024-3795(94)90351-4
10.1016/S0024-3795(96)00404-1
10.1016/0024-3795(81)90269-X
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10.1017/S0305004100052701
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Snippet 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...
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SubjectTerms AMS Subject Classification: 15A21
stabilizer; continuous/differentiable family
Structural stability
Title A generalized sylvester equation: a criterion for structural staility of triples of matrices
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Volume 44
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