Commuting Linear Operators and Decompositions; Applications to Einstein Manifolds

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F08%3A00035610" target="_blank" >RIV/00216224:14310/08:00035610 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Commuting Linear Operators and Decompositions; Applications to Einstein Manifolds
Original language description
For linear operators which factor P=P0 P1 ... Pp , with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same questions for the factors, or certain compositions thereof. When the operators Pi are polynomial in other commuting operators D1,...,Dk then we show that, in a suitable sense, generically such factorisation of Pi yield decompositions algebraically. In the case of operators on a vector space over an algebraically closed field this boils down to elementary algebraic geometry arising from the polynomial formula for P. The results and formulae are independent of the Dj and so the theory provides a routeto studying the solution space and the inhomogenous problem Pu=f without any attempt to 'diagonalise' the Dj.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/LC505" target="_blank" >LC505: Eduard Čech Center for Algebra and Geometry</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2008
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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