???? −Bernoulli Matrices and Their Some Properties

In this study, we define ???? −Bernoulli matrix Binsert ignore into journalissuearticles values( ); q and ???? −Bernoulli polynomial matrix Binsert ignore into journalissuearticles values( , ); x q by using ???? −Bernoulli numbers, and polynomials respectively. We obtain some properties of Binsert ignore into journalissuearticles values( ); q and Binsert ignore into journalissuearticles values( , ); x q . We obtain factorizations ???? −Bernoulli polynomial matrix and shifted ???? −Bernoulli matrix using special matrices.