Inverse of the Generalized Vandermonde Matrix via the Fundamental System of Linear difference Equations

In this study we display a process for inverting the generalized Vandermonde matrix, using the analytic properties of a fundamental system related to a specific linear difference equations. We establish two approaches allowing us to provide explicit formulas for the entries of the inverse of the generalized Vandermonde matrices. To enhance the effectiveness of our the approaches, significant examples and special cases are given.