Riordan arrays, Chebyshev polynomials, Fibonacci bases

Chebyshev polynomials and their modifications are attributes of various fields of mathematics. In particular, they are generating functions of the rows elements of certain Riordan matrices. In paper, we give a selection of some characteristic situations in which such matrices are involved. Using the columns and rows of these matrices, we will build the bases of the space of formal power series and the space of polynomials, the properties of which allow us to call them "Fibonacci bases".