Numerical range of a pair of strictly upper triangular matrices

Given two strictly upper triangular matrices X, Y ? Cm×m, we study the range W Y (X) = {trnXn-1Y* : n ? N}, where N is the group of unit upper triangular matrices in Cm×m. We prove that it is either a point or the whole complex plane. We characterize when it is a point. We also obtain some convexity...

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Autor principal:	Yan,Wen
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2011
Materias:	Numerical range unit upper triangular matrices strictly upper triangular matrices
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172011000100008
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spelling	oai:scielo:S0716-091720110001000082018-10-30Numerical range of a pair of strictly upper triangular matricesYan,Wen Numerical range unit upper triangular matrices strictly upper triangular matrices Given two strictly upper triangular matrices X, Y ? Cm×m, we study the range W Y (X) = {trnXn-1Y* : n ? N}, where N is the group of unit upper triangular matrices in Cm×m. We prove that it is either a point or the whole complex plane. We characterize when it is a point. We also obtain some convexity result for a similar range, where N is replaced by any ball of Ck (k = m(m - 1)/2) embedded in N , m = 4.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.30 n.1 20112011-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172011000100008en10.4067/S0716-09172011000100008
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Numerical range unit upper triangular matrices strictly upper triangular matrices
spellingShingle	Numerical range unit upper triangular matrices strictly upper triangular matrices Yan,Wen Numerical range of a pair of strictly upper triangular matrices
description	Given two strictly upper triangular matrices X, Y ? Cm×m, we study the range W Y (X) = {trnXn-1Y* : n ? N}, where N is the group of unit upper triangular matrices in Cm×m. We prove that it is either a point or the whole complex plane. We characterize when it is a point. We also obtain some convexity result for a similar range, where N is replaced by any ball of Ck (k = m(m - 1)/2) embedded in N , m = 4.
author	Yan,Wen
author_facet	Yan,Wen
author_sort	Yan,Wen
title	Numerical range of a pair of strictly upper triangular matrices
title_short	Numerical range of a pair of strictly upper triangular matrices
title_full	Numerical range of a pair of strictly upper triangular matrices
title_fullStr	Numerical range of a pair of strictly upper triangular matrices
title_full_unstemmed	Numerical range of a pair of strictly upper triangular matrices
title_sort	numerical range of a pair of strictly upper triangular matrices
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2011
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172011000100008
work_keys_str_mv	AT yanwen numericalrangeofapairofstrictlyuppertriangularmatrices
_version_	1718439774129225728

Numerical range of a pair of strictly upper triangular matrices

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