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Magnus expansion information


In mathematics and physics, the Magnus expansion, named after Wilhelm Magnus (1907–1990), provides an exponential representation of the product integral solution of a first-order homogeneous linear differential equation for a linear operator. In particular, it furnishes the fundamental matrix of a system of linear ordinary differential equations of order n with varying coefficients. The exponent is aggregated as an infinite series, whose terms involve multiple integrals and nested commutators.

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Magnus expansion

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In mathematics and physics, the Magnus expansion, named after Wilhelm Magnus (1907–1990), provides an exponential representation of the product integral...

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Matrix differential equation

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( s ) d s {\displaystyle \int _{a}^{t}\mathbf {A} (s)ds} then the Magnus expansion reduces to leading order, and the general solution to the differential...

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Wilhelm Magnus

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Hans Heinrich Wilhelm Magnus known as Wilhelm Magnus (5 February 1907 in Berlin, Germany – 15 October 1990 in New Rochelle, New York) was a German-American...

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Magnus Eriksson

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Magnus Eriksson (April or May 1316  – 1 December 1374) was King of Sweden from 1319 to 1364, King of Norway as Magnus VII from 1319 to 1355, and ruler...

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Magnus Magnusson

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Magnus Magnusson, KBE (born Magnús Sigursteinsson; 12 October 1929 – 7 January 2007) was an Icelandic-born British-based journalist, translator, writer...

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Product integral

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exponential. The Magnus expansion provides one technique for computing the Volterra integral. Examples include the Dyson expansion, the integrals that...

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Derivative of the exponential map

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frequently in physics for example in quantum field theory, as in the Magnus expansion in perturbation theory, and in lattice gauge theory. Throughout, the...

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Matrix exponential

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logarithm C0-semigroup Exponential function Exponential map (Lie theory) Magnus expansion Derivative of the exponential map Vector flow Golden–Thompson inequality...

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Linear differential equation

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use either a numerical method, or an approximation method such as Magnus expansion. Knowing the matrix U, the general solution of the non-homogeneous...

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Adductor magnus muscle

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the adductor magnus is considered a muscle of the posterior compartment of the thigh while the pubofemoral portion of the adductor magnus is considered...

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Ordered exponential

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the curvature tensor. Path-ordering (essentially the same concept) Magnus expansion Product integral Haar measure List of derivatives and integrals in...

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Viking expansion

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Viking expansion was the historical movement which led Norse explorers, traders and warriors, the latter known in modern scholarship as Vikings, to sail...

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Ultra Magnus

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trouble while attempting to discover Magnus' birthday. In addition to these and other battles with Cyclonus, Magnus also found himself facing Galvatron...

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Magnus Chase and the Gods of Asgard

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is the second book in the Magnus Chase and the Gods of Asgard series and was released on October 4, 2016. In this book, Magnus receives a quest from Otis...

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Vytautas Magnus University

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renamed in his honor (English: Vytautas Magnus University, Latin: Universitas Vytauti Magni). In 1940, Vytautas Magnus University contributed to the reestablishment...

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Query expansion

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1145/2851613.2851696 Sahlgren, Magnus, Jussi Karlgren, Rickard Cöster, and Timo Järvinen. 2003. "Automatic query expansion using random indexing." In Advances...

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Will Ferrell

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John William Ferrell (/ˈfɛrəl/; born July 16, 1967) is an American actor, comedian, writer, and producer. Ferrell is known for his leading man roles in...

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Heinrich Gustav Magnus

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use his first given name, and was known throughout his life as Gustav Magnus. Magnus was born in Berlin to a Jewish family, his father a wealthy merchant...

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Abdul Qadir Mumin

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International Crisis Group. 17 November 2016. Magnus Ranstorp; Filip Ahlin; Peder Hyllengren; Magnus Normark (2018). Mellan salafism och salafistisk...

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Vinland sagas

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Magnusson, Magnus (1976)Viking, Hammer of the North (Putnam) Magnus Magnusson ISBN 978-0-399-11744-2 Magnusson, Magnus (1979) Viking expansion westwards...

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Phase space crystal

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and the divergence problem is naturally avoided. To the lowest-order Magnus expansion for Floquet system, the quantum phase space interaction of two particles...

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Charlemagne

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Great"). In modern German, he is known as Karl der Große. The Latin epithet magnus ("great") may have been associated with him during his lifetime, but this...

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Donatus Magnus

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Donatus Magnus, also known as Donatus of Casae Nigrae, was the leader of a schismatic Christian sect known as the Donatists in North Africa, Algeria. He...

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Dyson series

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physics, the Dyson series, formulated by Freeman Dyson, is a perturbative expansion of the time evolution operator in the interaction picture. Each term can...

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