A matrix generalization of Euler identity e^(ix) = cosx + i sinx

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dc.creatorArgentini, Gianluca
dc.date2007-03-15
dc.date.accessioned2026-07-07T07:52:06Z
dc.date.available2026-07-07T07:52:06Z
dc.descriptionIn this work we present a matrix generalization of the Euler identity about exponential representation of a complex number. The concept of matrix exponential is used in a fundamental way. We define a notion of matrix imaginary unit which generalizes the usual complex imaginary unit. The Euler-like identity so obtained is compatible with the classical one. Also, we derive some exponential representation for matrix real and imaginary unit, and for the first Pauli matrix.
dc.description5 pages, research work done at R&D Dept. of Company Institution
dc.identifierhttps://arxiv.org/abs/math/0703448
dc.identifierhttp://arxiv.org/abs/math/0703448
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/125757
dc.subjectClassical Analysis and ODEs
dc.subjectMathematical Physics
dc.subjectGeneral Mathematics
dc.subjectFluid Dynamics
dc.subjectQuantum Physics
dc.subject15A24; 15A90
dc.titleA matrix generalization of Euler identity e^(ix) = cosx + i sinx
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