In this article, we introduce a Pascal functional matrix with four variables, where the (i, j)-th entry is the coefficient of \(t^{n-j}s^j\) in the expansion of \((xt+ys)^{n-i}(zt+ws)^i\) . The multiplication of the two Pascal functional matrices with four variables, the power and inverse of the Pascal functional matrix with four variables have very similar results to the well-known binomial matrix. The factorization of the Pascal functional matrix with four variables has also been given, which is completely similar to the factorization of the binomial matrix. Furthermore, two simple examples are given to show the application of the power and factorization properties of the Pascal functional matrix with four variables. Finally, we obtain the eigenvalues and eigenvectors of the Pascal functional matrix with four variables.
