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An umbral approach to find q-analogues of matrix formulasPrimeFaces.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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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2013 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 439, no 4, 1167-1182 p.Article in journal (Refereed) Published
##### Abstract [en]

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

2013. Vol. 439, no 4, 1167-1182 p.
##### Keyword [en]

NWA q-addition, Matrix power series, q-Cauchy-Vandermonde determinant, q-Stirling numbers, q-Exponential function, Ring, LU factorization
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:uu:diva-247672DOI: 10.1016/j.laa.2013.03.018ISI: 000321084700026OAI: oai:DiVA.org:uu-247672DiVA: diva2:797210
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Available from: 2015-03-23 Created: 2015-03-23 Last updated: 2015-03-23Bibliographically approved

A general introduction is given to the logarithmic q-analogue formulation of mathematical expressions with a special focus on its use for matrix calculations. The fundamental definitions relevant to q-analogues of mathematical objects are given and form the basis for matrix formulations in the paper. The umbral approach is used to find q-analogues of significant matrices. Finally, as an explicit example, a new formula for q-Cauchy-Vandermonde determinant containing matrix elements equal to q-numbers introduced by Ward is proved by using a new type of q-Stirling numbers together with Lagrange interpolation in Z(q).

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