| 释义 | ▪ I. Jacobian, a.1 and n. Math.|dʒəˈkəʊbɪən|
[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 determinant, Jacobian ellipsoid of equilibrium, Jacobian function, Jacobian system of differential equations.
B. n. (short for Jacobian determinant.) An important functional determinant, named after Jacobi.
The constituents of the determinant 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,..) .
1852Sylvester in Camb. & 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.
▪ II. Jacobian, a.2 rare.|dʒəˈkəʊbɪən|
[f. L. Jacōb-us + -ian: cf. Jacobean.]
a. Of or pertaining to the patriarch Jacob.
b. = Jacobean 1 a.
1865F. H. Laing in Manning Ess. Relig. & Lit. I. 208 The race of Israel proper, the genuine Jacobian breed. 1883Wallenstein in the Drama in Westm. Rev., Dramatic work of the Elizabethan and Jacobian times. |
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