# Factorizations for q-Pascal matrices of two variables

Special Matrices (2015)

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

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topThomas 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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- [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] 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] T. Ernst, A comprehensive treatment of q-calculus, Birkhäuser 2012. Zbl1256.33001
- [6] T. Ernst, An umbral approach to find q-analogues of matrix formulas, Linear Algebra Appl. 439 (2013), 1167–1182. [WoS] Zbl1305.15039
- [7] T. Ernst, Faktorisierungen von q-Pascalmatrizen (Factorizations of q-Pascal matrices), Algebras Groups Geom. 31 (2014), no. 4, 387-405 Zbl1317.15012
- [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. Zbl35.0445.01
- [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] M. Ward, A calculus of sequences, Amer. J. Math. 58 (1936), 255–266. Zbl62.0408.03
- [12] Z. Zhang, The linear algebra of the generalized Pascal matrix, Linear Algebra Appl. 250 (1997), 51–60. Zbl0873.15014
- [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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