Noncommutative Spectral Decomposition with Quasideterminant

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dc.creatorSuzuki, Tatsuo
dc.date2007-03-26
dc.date.accessioned2026-07-07T07:53:54Z
dc.date.available2026-07-07T07:53:54Z
dc.descriptionWe develop a noncommutative analogue of the spectral decomposition with the quasideterminant defined by I. Gelfand and V. Retakh. In this theory, by introducing a noncommutative Lagrange interpolating polynomial and combining a noncommutative Cayley-Hamilton's theorem and an identity given by a Vandermonde-like quasideterminant, we can systematically calculate a function of a matrix even if it has noncommutative entries. As examples, the noncommutative spectral decomposition and the exponential matrices of a quaternionic matrix and of a matrix with entries being harmonic oscillators are given.
dc.description18 pages, no figures
dc.identifierhttps://arxiv.org/abs/math/0703751
dc.identifierhttp://arxiv.org/abs/math/0703751
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126403
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.subjectQuantum Physics
dc.titleNoncommutative Spectral Decomposition with Quasideterminant
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