A new extension of generalized Pascal-type matrix and their representations via Riordan matrix

The algebraic approach based on Pascal matrices is important in many fields of mathematics, ranging from algebraic geometry to optimization, matrix theory and combinatorics. The core of the proposed approach is to introduce a new family of Pascal-type matrices Ψi,j,c,a[x,y],x,y∈R-{0} with parameters...

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Autores:: Ramírez, William
Urieles, Alejandro
Riyasat, Mumtaz
Ortega Wilches, María José
Siado, Luis

Tipo de recurso:: Article of investigation

Fecha de publicación:: 2024

Institución:: Corporación Universidad de la Costa

Repositorio:: REDICUC - Repositorio CUC

Idioma:: eng

Description
Summary:	The algebraic approach based on Pascal matrices is important in many fields of mathematics, ranging from algebraic geometry to optimization, matrix theory and combinatorics. The core of the proposed approach is to introduce a new family of Pascal-type matrices Ψi,j,c,a[x,y],x,y∈R-{0} with parameters c,a∈R+-{1}. By employing the effective matrix algebra tools, certain algebraic properties including the product formula, inverse matrix, determinant and eigen values are determined for the Pascal matrix Ψi,j,c,a[x,y]. Further, some new families of matrices like the Fibonacci Fi,j,c,a[x,y], Lucas Li,j,c,a[x,y], Pell Si,j,c,a[x,y] and other matrices are introduced and these are employed to derive factorization formulae for the Pascal matrix Ψi,j,c,a[x,y] involving Riordan matrix. Finally, the properties and representations derived above for these matrices are further demonstrated for a matrix of particular order 3.

A new extension of generalized Pascal-type matrix and their representations via Riordan matrix

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