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An umbral approach to find q-analogues of matrix formulas
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
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]

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).

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
Available from: 2015-03-23 Created: 2015-03-23 Last updated: 2017-12-04Bibliographically approved

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