Matches in SemOpenAlex for { <https://semopenalex.org/work/W2069576326> ?p ?o ?g. }
Showing items 1 to 100 of
100
with 100 items per page.
- W2069576326 abstract "Abstract A complex matrix is said to be stable if all its eigenvalues have negative real part. Let J be a Jordan block with zeros on the diagonal and ones on the superdiagonal, and consider analytic matrix perturbations of the form A ( e ) = J + eB + O ( e 2 ), where e is real and positive. A necessary condition on B for the stability of A (e) on an interval (0, e 0 ), and a sufficient condition on B for the existence of such a family A (e), is (i) Re tr B ⩽ 0; (ii) the sum of the elements on the first subdiagonal of B has nonpositive real part and zero imaginary part; (iii) the sum of the elements on each of the other subdiagonals of B is zero. This result is extended to matrices with any number of nonderogatory eigenvalues on the imaginary axis, and to a stability definition based on the spectral radius. A generalized necessary condition, though not a sufficient condition, applies to arbitrary Jordan structures. The proof of our results uses two important techniques: the Puiseux-Newton diagram and the Arnold normal form. In the non-deragatory case our main results were obtained by Levantovskii in 1980 using a different proof. Practical implications are discussed." @default.
- W2069576326 created "2016-06-24" @default.
- W2069576326 creator A5069099932 @default.
- W2069576326 creator A5085980354 @default.
- W2069576326 date "2011-09-03" @default.
- W2069576326 modified "2023-09-27" @default.
- W2069576326 title "Stable perturbations of nonsymmetric matrices" @default.
- W2069576326 cites W1563885070 @default.
- W2069576326 cites W1575147392 @default.
- W2069576326 cites W1969125683 @default.
- W2069576326 cites W1982604350 @default.
- W2069576326 cites W1993122364 @default.
- W2069576326 cites W1994003764 @default.
- W2069576326 cites W2012593533 @default.
- W2069576326 cites W2013257649 @default.
- W2069576326 cites W2013737143 @default.
- W2069576326 cites W2025639042 @default.
- W2069576326 cites W2036312716 @default.
- W2069576326 cites W2128949314 @default.
- W2069576326 cites W2128978199 @default.
- W2069576326 cites W2599521437 @default.
- W2069576326 cites W2617854063 @default.
- W2069576326 cites W2798909945 @default.
- W2069576326 hasPublicationYear "2011" @default.
- W2069576326 type Work @default.
- W2069576326 sameAs 2069576326 @default.
- W2069576326 citedByCount "7" @default.
- W2069576326 countsByYear W20695763262013 @default.
- W2069576326 crossrefType "book" @default.
- W2069576326 hasAuthorship W2069576326A5069099932 @default.
- W2069576326 hasAuthorship W2069576326A5085980354 @default.
- W2069576326 hasConcept C106487976 @default.
- W2069576326 hasConcept C112972136 @default.
- W2069576326 hasConcept C113313756 @default.
- W2069576326 hasConcept C119857082 @default.
- W2069576326 hasConcept C121332964 @default.
- W2069576326 hasConcept C130367717 @default.
- W2069576326 hasConcept C134306372 @default.
- W2069576326 hasConcept C138885662 @default.
- W2069576326 hasConcept C140532419 @default.
- W2069576326 hasConcept C158693339 @default.
- W2069576326 hasConcept C159985019 @default.
- W2069576326 hasConcept C179117685 @default.
- W2069576326 hasConcept C192562407 @default.
- W2069576326 hasConcept C202444582 @default.
- W2069576326 hasConcept C2524010 @default.
- W2069576326 hasConcept C2780813799 @default.
- W2069576326 hasConcept C33923547 @default.
- W2069576326 hasConcept C41008148 @default.
- W2069576326 hasConcept C41895202 @default.
- W2069576326 hasConcept C62520636 @default.
- W2069576326 hasConcept C89890916 @default.
- W2069576326 hasConceptScore W2069576326C106487976 @default.
- W2069576326 hasConceptScore W2069576326C112972136 @default.
- W2069576326 hasConceptScore W2069576326C113313756 @default.
- W2069576326 hasConceptScore W2069576326C119857082 @default.
- W2069576326 hasConceptScore W2069576326C121332964 @default.
- W2069576326 hasConceptScore W2069576326C130367717 @default.
- W2069576326 hasConceptScore W2069576326C134306372 @default.
- W2069576326 hasConceptScore W2069576326C138885662 @default.
- W2069576326 hasConceptScore W2069576326C140532419 @default.
- W2069576326 hasConceptScore W2069576326C158693339 @default.
- W2069576326 hasConceptScore W2069576326C159985019 @default.
- W2069576326 hasConceptScore W2069576326C179117685 @default.
- W2069576326 hasConceptScore W2069576326C192562407 @default.
- W2069576326 hasConceptScore W2069576326C202444582 @default.
- W2069576326 hasConceptScore W2069576326C2524010 @default.
- W2069576326 hasConceptScore W2069576326C2780813799 @default.
- W2069576326 hasConceptScore W2069576326C33923547 @default.
- W2069576326 hasConceptScore W2069576326C41008148 @default.
- W2069576326 hasConceptScore W2069576326C41895202 @default.
- W2069576326 hasConceptScore W2069576326C62520636 @default.
- W2069576326 hasConceptScore W2069576326C89890916 @default.
- W2069576326 hasLocation W20695763261 @default.
- W2069576326 hasOpenAccess W2069576326 @default.
- W2069576326 hasPrimaryLocation W20695763261 @default.
- W2069576326 hasRelatedWork W1563885070 @default.
- W2069576326 hasRelatedWork W1564725221 @default.
- W2069576326 hasRelatedWork W1575147392 @default.
- W2069576326 hasRelatedWork W1969662777 @default.
- W2069576326 hasRelatedWork W1993068751 @default.
- W2069576326 hasRelatedWork W2002986350 @default.
- W2069576326 hasRelatedWork W2009871339 @default.
- W2069576326 hasRelatedWork W2015321063 @default.
- W2069576326 hasRelatedWork W2028289630 @default.
- W2069576326 hasRelatedWork W2032815046 @default.
- W2069576326 hasRelatedWork W2036312716 @default.
- W2069576326 hasRelatedWork W2050134679 @default.
- W2069576326 hasRelatedWork W2058172093 @default.
- W2069576326 hasRelatedWork W2075334209 @default.
- W2069576326 hasRelatedWork W2076824500 @default.
- W2069576326 hasRelatedWork W2081395081 @default.
- W2069576326 hasRelatedWork W2084300474 @default.
- W2069576326 hasRelatedWork W2110300552 @default.
- W2069576326 hasRelatedWork W2115172831 @default.
- W2069576326 hasRelatedWork W2128978199 @default.
- W2069576326 isParatext "false" @default.
- W2069576326 isRetracted "false" @default.
- W2069576326 magId "2069576326" @default.
- W2069576326 workType "book" @default.