Bernoulli matrix and its algebraic properties Original Research Article

In this paper, we define the generalized Bernoulli polynomial matrix image and the Bernoulli matrix image. Using some properties of Bernoulli polynomials and numbers, a product formula of image and the inverse of image were given. It is shown that not only image, where image is the generalized Pascal matrix, but also image, where image is the Fibonacci matrix, image and image are the image lower triangular matrices whose image-entries are image and image, respectively. From these formulas, several interesting identities involving the Fibonacci numbers and the Bernoulli polynomials and numbers are obtained. The relationships are established about Bernoulli, Fibonacci and Vandermonde matrices.