Partial Differential Operator on Vector Space of Polynomials

Abstract

A differential operator which acts on partial differentiation is defined as Partial Differential Operator (PDO). PDO works based on the order of the differential equation which then can solve the eigenvalues of the operator. On vector space of polynomials, PDO can be written in matrix representation. This can be helpful in finding the general form of eigenvalues of vector space polynomials. On this paper, a second order PDO:

will be operated on two and three variable vector space polynomials.