Math. [f. Jacobi, proper name + -AN.]
A. adj. Pertaining to or named after the mathematician K. G. J. Jacobi (1804–51), professor at Königsberg in Prussia; discovered, introduced or investigated by Jacobi; as Jacobian ellipsoid of equilibrium, Jacobian function, Jacobian system of differential equations. B. sb. (short for Jacobian determinant.) An important functional determinant, named after Jacobi.
Its constituents are the differential coefficients of any number of functions (u, v, w,…) with respect to the same number of variables (x, y, z,…); it vanishes when the functions are connected by any relation of the form F (u, v, w,…) = 0. It is usually denoted by d (u, v, w,…)/d (x, y, z,…).
1852. Sylvester, in Cambr. & Dubl. Math. Jrnl., VII. 71–2.
1881. Encycl. Brit., XIII. 31. Such functional determinants are now more usually known as Jacobians, a designation introduced by Professor Sylvester, who largely developed their properties, and gave numerous applications of them in higher algebra, as also in curves and surfaces.
