Factorizations for q-Pascal matrices of two variables

• Autorzy: Thomas Ernst
• Języki publikacji: EN

Abstrakty

EN

In this second article on q-Pascal matrices, we show how the previous factorizations by the summation matrices and the so-called q-unit matrices extend in a natural way to produce q-analogues of Pascal matrices of two variables by Z. Zhang and M. Liu as follows [...] We also find two different matrix products for [...]

Słowa kluczowe

EN

q-Pascal matrix; q-unit matrix; q-matrix multiplication

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-07-15

zaakceptowano

2015-09-14

online

2015-10-06

Twórcy

autor

Thomas Ernst

• Department of Mathematics, Uppsala University, P.O. Box 480, SE-751 06 Uppsala, Sweden

Bibliografia

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• [2] R. Brawer and M. Pirovino, The linear algebra of the Pascal matrix, Linear Algebra Appl. 174 (1992), 13–23.
• [3] T. Ernst, q-Leibniz functional matrices with applications to q-Pascal and q-Stirling matrices, Adv. Stud. Contemp. Math., Kyungshang 22 (2012), 537-555.
• [4] T. Ernst, q-Pascal and q-Wronskian matrices with implications to q-Appell polynomials, J. Discrete Math., (2013), Article ID 450481, 10 p.
• [5] T. Ernst, A comprehensive treatment of q-calculus, Birkhäuser 2012.
• [6] T. Ernst, An umbral approach to find q-analogues of matrix formulas, Linear Algebra Appl. 439 (2013), 1167–1182. [WoS]
• [7] T. Ernst, Faktorisierungen von q-Pascalmatrizen (Factorizations of q-Pascal matrices), Algebras Groups Geom. 31 (2014), no. 4, 387-405
• [8] H. Exton, q-Hypergeometric functions and applications, Ellis Horwood 1983.
• [9] F.H. Jackson, A basic-sine and cosine with symbolical solution of certain differential equations, Proc. EdinburghMath. Soc. 22 (1904), 28–39.
• [10] P. Nalli, On a calculation procedure similar to integration, (Sopra un procedimento di calcolo analogo all integrazione) (Italian), Palermo Rend 47 (1923), 337–374.
• [11] M. Ward, A calculus of sequences, Amer. J. Math. 58 (1936), 255–266.
• [12] Z. Zhang, The linear algebra of the generalized Pascal matrix, Linear Algebra Appl. 250 (1997), 51–60.
• [13] Z. Zhang and M. Liu, An extension of the generalized Pascal matrix and its algebraic properties, Linear Algebra Appl. 271 (1998), 169–177.

Identyfikatory

DOI

10.1515/spma-2015-0020