Factorizations for q-Pascal matrices of two variables

Thomas Ernst

Special Matrices (2015)

  • Volume: 3, Issue: 1, page 207-213, electronic only
  • ISSN: 2300-7451

Abstract

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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 [...]

How to cite

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Thomas Ernst. "Factorizations for q-Pascal matrices of two variables." Special Matrices 3.1 (2015): 207-213, electronic only. <http://eudml.org/doc/275897>.

@article{ThomasErnst2015,
abstract = {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 [...]},
author = {Thomas Ernst},
journal = {Special Matrices},
keywords = {q-Pascal matrix; q-unit matrix; q-matrix multiplication; -Pascal matrix; -unit matrix; -matrix multiplication},
language = {eng},
number = {1},
pages = {207-213, electronic only},
title = {Factorizations for q-Pascal matrices of two variables},
url = {http://eudml.org/doc/275897},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Thomas Ernst
TI - Factorizations for q-Pascal matrices of two variables
JO - Special Matrices
PY - 2015
VL - 3
IS - 1
SP - 207
EP - 213, electronic only
AB - 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 [...]
LA - eng
KW - q-Pascal matrix; q-unit matrix; q-matrix multiplication; -Pascal matrix; -unit matrix; -matrix multiplication
UR - http://eudml.org/doc/275897
ER -

References

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  1. [1] W. A. Al-Salam, q-Bernoulli numbers and polynomials, Math. Nachr 17 (1959), 239–260. [Crossref] 
  2. [2] R. Brawer and M. Pirovino, The linear algebra of the Pascal matrix, Linear Algebra Appl. 174 (1992), 13–23. Zbl0755.15012
  3. [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. Zbl1279.15013
  4. [4] T. Ernst, q-Pascal and q-Wronskian matrices with implications to q-Appell polynomials, J. Discrete Math., (2013), Article ID 450481, 10 p. Zbl1295.05060
  5. [5] T. Ernst, A comprehensive treatment of q-calculus, Birkhäuser 2012. Zbl1256.33001
  6. [6] T. Ernst, An umbral approach to find q-analogues of matrix formulas, Linear Algebra Appl. 439 (2013), 1167–1182. [WoS] Zbl1305.15039
  7. [7] T. Ernst, Faktorisierungen von q-Pascalmatrizen (Factorizations of q-Pascal matrices), Algebras Groups Geom. 31 (2014), no. 4, 387-405 Zbl1317.15012
  8. [8] H. Exton, q-Hypergeometric functions and applications, Ellis Horwood 1983. 
  9. [9] F.H. Jackson, A basic-sine and cosine with symbolical solution of certain differential equations, Proc. EdinburghMath. Soc. 22 (1904), 28–39. Zbl35.0445.01
  10. [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. Zbl49.0196.02
  11. [11] M. Ward, A calculus of sequences, Amer. J. Math. 58 (1936), 255–266. Zbl62.0408.03
  12. [12] Z. Zhang, The linear algebra of the generalized Pascal matrix, Linear Algebra Appl. 250 (1997), 51–60. Zbl0873.15014
  13. [13] Z. Zhang and M. Liu, An extension of the generalized Pascal matrix and its algebraic properties, Linear Algebra Appl. 271 (1998), 169–177. Zbl0892.15018

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