The linear algebra of a Pascal-like matrix

Abstract

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.

Keywords:

• Pascal-like matrix
• factorials and binomial coefficients
• matrix inversion
• Hermite polynomial
• factorization of a matrix
• Toeplitz matrix

AMS CLASSIFICATIONS:

• 05A10
• 15A09
• 11C08
• 15A23
• 15B05

Acknowledgments

The authors would like to thank the referees for their valuable comments which helped to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.