Characteristic parameter sets and limits of circulant Hermitian polygon transformations

Vartziotis, D; Wipper, J

dc.contributor.author	Vartziotis, D	en
dc.contributor.author	Wipper, J	en
dc.date.accessioned	2014-03-01T01:32:59Z
dc.date.available	2014-03-01T01:32:59Z
dc.date.issued	2010	en
dc.identifier.issn	0024-3795	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20265
dc.subject	Circulant matrix	en
dc.subject	Eigenpolygon	en
dc.subject	Hermitian matrix	en
dc.subject	Limit polygon	en
dc.subject	Napoleon's theorem	en
dc.subject	Petr-Douglas-Neumann theorem	en
dc.subject	Polygon transformation	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Basic transformations	en
dc.subject.other	Characteristic parameter	en
dc.subject.other	Circulant matrix	en
dc.subject.other	Circulants	en
dc.subject.other	Construction parameter	en
dc.subject.other	Douglas	en
dc.subject.other	Finite set	en
dc.subject.other	Hermitian matrices	en
dc.subject.other	Hermitians	en
dc.subject.other	Linear combinations	en
dc.subject.other	Rotational effects	en
dc.subject.other	Sub-domains	en
dc.title	Characteristic parameter sets and limits of circulant Hermitian polygon transformations	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.laa.2010.04.022	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.laa.2010.04.022	en
heal.language	English	en
heal.publicationDate	2010	en
heal.abstract	Polygon transformations based on taking the apices of similar triangles constructed on the sides of an initial polygon are analyzed as well as the limit polygons obtained by iteratively applying such transformations. In contrast to other approaches, this is done with respect to two construction parameters representing a base angle and an apex perpendicular subdivision ratio. Furthermore, a combined transformation leading to circulant Hermitian matrices is proposed, which eliminates the rotational effect of the basic transformation. A finite set of characteristic parameter subdomains is derived for which the sequence converges to specific eigenpolygons. Otherwise, limit polygons turn out to be linear combinations of up to three eigenpolygons. This leads to a full classification of circulant Hermitian similar triangles based polygon transformations and their limit polygons. As a byproduct classical results as Napoleon's theorem and the Petr-Douglas-Neumann theorem can be easily deduced. (C) 2010 Elsevier Inc. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE INC	en
heal.journalName	Linear Algebra and Its Applications	en
dc.identifier.doi	10.1016/j.laa.2010.04.022	en
dc.identifier.isi	ISI:000279413600007	en
dc.identifier.volume	433	en
dc.identifier.issue	5	en
dc.identifier.spage	945	en
dc.identifier.epage	955	en