Operator-valued semicircular elements: Solving a quadratic matrix equation with positivity constraints

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dc.creatorHelton, J. William
dc.creatorFar, Reza Rashidi
dc.creatorSpeicher, Roland
dc.date2007-03-17
dc.date.accessioned2026-07-07T07:52:34Z
dc.date.available2026-07-07T07:52:34Z
dc.descriptionWe show that the quadratic matrix equation $VW + η(W)W = I$, for given $V$ with positive real part and given analytic mapping $η$ with some positivity preserving properties, has exactly one solution $W$ with positive real part. We point out the relevance of this result in the context of operator-valued free probability theory and for the determination of the asymptotic eigenvalue distribution of band or block random matrices. We also address the problem of a numerical determination of the solution.
dc.description14 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/math/0703510
dc.identifierhttp://arxiv.org/abs/math/0703510
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/125926
dc.subjectOperator Algebras
dc.subjectComplex Variables
dc.titleOperator-valued semicircular elements: Solving a quadratic matrix equation with positivity constraints
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