Isospectral flows on a class of finite-dimensional Jacobi matrices

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SUTTER, Tobias, Debasish CHATTERJEE, Federico A. RAMPONI, John LYGEROS, 2013. Isospectral flows on a class of finite-dimensional Jacobi matrices. In: Systems & Control Letters. Elsevier. 62(5), pp. 388-394. ISSN 0167-6911. eISSN 1872-7956. Available under: doi: 10.1016/j.sysconle.2013.02.004

@article{Sutter2013Isosp-55735, title={Isospectral flows on a class of finite-dimensional Jacobi matrices}, year={2013}, doi={10.1016/j.sysconle.2013.02.004}, number={5}, volume={62}, issn={0167-6911}, journal={Systems & Control Letters}, pages={388--394}, author={Sutter, Tobias and Chatterjee, Debasish and Ramponi, Federico A. and Lygeros, John}, note={19 pages, 3 figures, conjecture from previous version is added as assertion (iv) of the main theorem including a proof; other major changes} }

<rdf:RDF xmlns:dcterms="" xmlns:dc="" xmlns:rdf="" xmlns:bibo="" xmlns:dspace="" xmlns:foaf="" xmlns:void="" xmlns:xsd="" > <rdf:Description rdf:about=""> <dc:contributor>Lygeros, John</dc:contributor> <dcterms:isPartOf rdf:resource=""/> <dcterms:rights rdf:resource=""/> <dc:contributor>Ramponi, Federico A.</dc:contributor> <dc:creator>Chatterjee, Debasish</dc:creator> <dc:language>eng</dc:language> <dcterms:abstract xml:lang="eng">We present a new matrix-valued isospectral ordinary differential equation that asymptotically block-diagonalizes n x n zero-diagonal Jacobi matrices employed as its initial condition. This o.d.e. features a right-hand side with a nested commutator of matrices and structurally resembles the double-bracket o.d.e. studied by R.W. Brockett in 1991. We prove that its solutions converge asymptotically, that the limit is block-diagonal, and above all, that the limit matrix is defined uniquely as follows: for n even, a block-diagonal matrix containing 2 x 2 blocks, such that the super-diagonal entries are sorted by strictly increasing absolute value. Furthermore, the off-diagonal entries in these 2 x 2 blocks have the same sign as the respective entries in the matrix employed as the initial condition. For odd, there is one additional 1 x 1 block containing a zero that is the top left entry of the limit matrix. The results presented here extend some early work of Kac and van Moerbeke.</dcterms:abstract> <dc:creator>Lygeros, John</dc:creator> <dcterms:available rdf:datatype="">2021-12-02T12:22:38Z</dcterms:available> <dc:creator>Sutter, Tobias</dc:creator> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dc:contributor>Sutter, Tobias</dc:contributor> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dc:contributor>Chatterjee, Debasish</dc:contributor> <dc:rights>terms-of-use</dc:rights> <dspace:isPartOfCollection rdf:resource=""/> <bibo:uri rdf:resource=""/> <dcterms:title>Isospectral flows on a class of finite-dimensional Jacobi matrices</dcterms:title> <dc:date rdf:datatype="">2021-12-02T12:22:38Z</dc:date> <dcterms:issued>2013</dcterms:issued> <dc:creator>Ramponi, Federico A.</dc:creator> </rdf:Description> </rdf:RDF>

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