Positive eigenvalues and two-letter generalized words

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dc.creatorHillar, Christopher
dc.creatorJohnson, Charles R.
dc.creatorSpitkovsky, Ilya M.
dc.date2005-04-28
dc.date.accessioned2026-07-07T05:19:28Z
dc.date.available2026-07-07T05:19:28Z
dc.descriptionA generalized word in two letters $A$ and $B$ is an expression of the form $W=A^{α_1}B^{β_1}A^{α_2}B^{β_2}... A^{α_N}B^{β_N}$ in which the exponents $α_i$, $β_i$ are nonzero real numbers. When independent positive definite matrices are substituted for $A$ and $B$, we are interested in whether $W$ necessarily has positive eigenvalues. This is known to be the case when N=1 and has been studied in case all exponents are positive by two of the authors. When the exponent signs are mixed, however, the situation is quite different (even for 2-by-2 matrices), and this is the focus of the present work.
dc.description6 Pages, Electronic Journal of Linear Algebra
dc.identifierhttps://arxiv.org/abs/math/0504573
dc.identifierhttp://arxiv.org/abs/math/0504573
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75031
dc.subjectOperator Algebras
dc.subjectRings and Algebras
dc.subject15A18, 15A57
dc.titlePositive eigenvalues and two-letter generalized words
dc.typetext

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