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Lundengård, KarlSilvestrov, Sergei
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Extreme points of the Vandermonde determinant on the sphere and some limits involving the generalized Vandermonde determinantPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2020 (English)In: Algebraic Structures and Applications / [ed] Sergei Silvestrov, Anatoliy Malyarenko, Milica Rancic, Springer Nature, 2020, , p. 28p. 761-789Chapter in book (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Springer Nature, 2020. , p. 28p. 761-789
##### Series

Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009, E-ISSN 2194-1017 ; 317
##### Keywords [en]

Vandermonde matrix, Determinants, Extreme points, Unit sphere, Generalized Vandermonde matrix
##### National Category

Mathematical Analysis
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

URN: urn:nbn:se:mdh:diva-23914DOI: 10.1007/978-3-030-41850-2_32Scopus ID: 2-s2.0-85087531998ISBN: 978-3-030-41849-6 (print)ISBN: 978-3-030-41850-2 (electronic)OAI: oai:DiVA.org:mdh-23914DiVA, id: diva2:682307
##### Conference

International Conference on Stochastic Processes and Algebraic Structures, SPAS 2017; Västerås and Stockholm; Sweden; 4 October 2017 through 6 October 2017; Code 241139
#####

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##### Funder

Swedish Research CouncilAvailable from: 2013-12-27 Created: 2013-12-21 Last updated: 2020-09-30Bibliographically approved
##### In thesis

The values of the determinant of Vandermonde matrices with real elements are analyzed both visually and analytically over the unit sphere in various dimensions. For three dimensions some generalized Vandermonde matrices are analyzed visually. The extreme points of the ordinary Vandermonde determinant on finite-dimensional unit spheres are given as the roots of rescaled Hermite polynomials and a recursion relation is provided for the polynomial coefficients. Analytical expressions for these roots are also given for dimension three to seven. A transformation of the optimization problem is provided and some relations between the ordinary and generalized Vandermonde matrices involving limits are discussed.

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