q - Bernoulli Matrices and Their Some Properties

Abstract

In this study, we defineq - Bernoulli matrix B(q) and q-Bernoulli polynomial matrix B(x,q) by using q -Bernoulli numbers, and polynomials respectively. We obtain some properties of B (q) and B(x,q) We obtain factorizations q -Bernoulli polynomial matrix and shifted q -Bernoulli matrix using special matrices.