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The linear algebra of a Pascal-like matrix
(TAYLOR & FRANCIS LTD, 2020) Zheng, De-Yin; Akkus, Ilker; Kizilaslan, Gonca
A Pascal-like matrix is constructed whose row entries are the terms of the modified Hermite polynomials of two variables. The multiplication of the two Pascal-like matrices and the power and inverse of the Pascal-like matrix have very similar results to the well-known Binomial Matrix, and the factorization of the Pascal-like matrix has also been given, which is completely similar to the factorization of Binomial Matrix. Furthermore, two simple examples are given to show the application of the power and factorization properties of the Pascal-like matrix. Finally, a generalization of the Pascal-like matrix is given and some combinatorial identities are obtained such as Tepper-like identity.
NEW REPRESENTATIONS OF PASCAL MATRIX VIA OPERATIONAL q-CALCULUS
(Honam Mathematical Soc, 2022) Zheng, De-Yin; Akkus, Ilker; Kizilaslan, Gonca
In this paper we introduce two type of representations of the Pascal matrix via induced transformations of some q-derivatives as well as their some combinatorial applications.