for the operator the coefficients are For instance, the operator is factorizable as and its transpose is factorizable then as See also Partial derivative Invariant (mathematics) Invariant theory Characteristic polynomial Notes References J. Weiss. Bäcklund transformation and the Painlevé property. J. Math. Phys. 27, 1293-1305 (1986). R. Beals, E. Kartashova. Constructively factoring linear partial differential operators in two variables. Theor. Math. Phys. 145(2), pp. 1510-1523 (2005) E. Kartashova. A Hierarchy of Generalized Invariants for Linear Partial Differential Operators. Theor. Math. Phys. 147(3), pp. 839-846 (2006) E. Kartashova, O. Rudenko. Invariant Form of BK-factorization and its Applications. Proc. GIFT-2006, pp.225-241, Eds.: J. Calmet, R. W. Tucker, Karlsruhe University Press (2006); arXiv Multivariable calculus Differential operators Partial differential equations