Jacobianadj.¹n.

/dʒəˈkəʊbɪən/

Etymology: < the name of the professor and mathematician K. G. J. Jacobi (1804–51), of Königsberg, East Prussia (now Kaliningrad, Russia) + -an suffix.

Mathematics.

A. adj.¹

Relating to or named after Jacobi; discovered, introduced, or investigated by Jacobi; as Jacobian determinant, Jacobian ellipsoid of equilibrium, Jacobian function, Jacobian system of differential equations.

ΚΠ

1852 Sylvester in Cambr. & Dublin Math. Jrnl. VII. 71 The Jacobian determinant.

B. n. (short for Jacobian determinant at sense A.)

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,..)}.

ΘΚΠ

the world > relative properties > number > algebra > [noun] > expression > function > covariance or covariant

Jacobian1852

covariant1853

Hessian1856

transmutant1858

transvectant1876

covariance1878

segregate1878

covariancy1895

the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > array > matrix > operation or result of > determinant

determinant1843

hyperdeterminant1845

Jacobian1852

circulant1881

1852 Sylvester in Cambr. & Dublin Math. Jrnl. VII. 72 The Jacobian R is of the degree 3n - 4.

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.

This entry has not yet been fully updated (first published 1900; most recently modified version published online June 2018).

Jacobianadj.²

/dʒəˈkəʊbɪən/

Etymology: < Latin Jacōbus + -ian suffix: compare Jacobean adj. and n.

rare.

a. Of or pertaining to the patriarch Jacob.

ΘΚΠ

society > society and the community > kinship or relationship > kinsman or relation > ancestor > [adjective] > of patriarchs > specific

Abrahamical1683

Abrahamic1699

Jacobian1865

Sethic1883

1865 F. H. Laing in H. E. Manning Ess. Relig. & Lit. I. 208 The race of Israel proper, the genuine Jacobian breed.

b. = Jacobean adj. 1a.

ΘΚΠ

the world > time > relative time > the past > historical period > [adjective] > of other specific periods

Georgian1745

romancean1804

early modern1817

federal1838

Jacobean1844

post-Reformation1850

pre-Reformation1855

postcolonial1861

post-Renaissance1874

post-conquest1880

post-conquestual1880

Jacobian1883

post-pyramidal1883

pre-industrial1883

early American1895

bow-and-arrow1899

palaeotechnic1904

Renaissancist1932

steam age1941

Carolinian1949

postcolonialist1957

1883 Wallenstein in the Drama in Westm. Rev. Dramatic work of the Elizabethan and Jacobian times.

This entry has not yet been fully updated (first published 1900; most recently modified version published online March 2018).

单词	jacobian
释义	Jacobianadj.¹n. /dʒəˈkəʊbɪən/ Etymology: < the name of the professor and mathematician K. G. J. Jacobi (1804–51), of Königsberg, East Prussia (now Kaliningrad, Russia) + -an suffix. Mathematics. A. adj.¹ Relating to or named after Jacobi; discovered, introduced, or investigated by Jacobi; as Jacobian determinant, Jacobian ellipsoid of equilibrium, Jacobian function, Jacobian system of differential equations. ΚΠ 1852 Sylvester in Cambr. & Dublin Math. Jrnl. VII. 71 The Jacobian determinant. B. n. (short for Jacobian determinant at sense A.) 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,..)}. ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > function > covariance or covariant Jacobian1852 covariant1853 Hessian1856 transmutant1858 transvectant1876 covariance1878 segregate1878 covariancy1895 the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > array > matrix > operation or result of > determinant determinant1843 hyperdeterminant1845 Jacobian1852 circulant1881 1852 Sylvester in Cambr. & Dublin Math. Jrnl. VII. 72 The Jacobian R is of the degree 3n - 4. 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. This entry has not yet been fully updated (first published 1900; most recently modified version published online June 2018). Jacobianadj.² /dʒəˈkəʊbɪən/ Etymology: < Latin Jacōbus + -ian suffix: compare Jacobean adj. and n. rare. a. Of or pertaining to the patriarch Jacob. ΘΚΠ society > society and the community > kinship or relationship > kinsman or relation > ancestor > [adjective] > of patriarchs > specific Abrahamical1683 Abrahamic1699 Jacobian1865 Sethic1883 1865 F. H. Laing in H. E. Manning Ess. Relig. & Lit. I. 208 The race of Israel proper, the genuine Jacobian breed. b. = Jacobean adj. 1a. ΘΚΠ the world > time > relative time > the past > historical period > [adjective] > of other specific periods Georgian1745 romancean1804 early modern1817 federal1838 Jacobean1844 post-Reformation1850 pre-Reformation1855 postcolonial1861 post-Renaissance1874 post-conquest1880 post-conquestual1880 Jacobian1883 post-pyramidal1883 pre-industrial1883 early American1895 bow-and-arrow1899 palaeotechnic1904 Renaissancist1932 steam age1941 Carolinian1949 postcolonialist1957 1883 Wallenstein in the Drama in Westm. Rev. Dramatic work of the Elizabethan and Jacobian times. This entry has not yet been fully updated (first published 1900; most recently modified version published online March 2018). < adj.¹n.1852adj.²1865
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Jacobianadj.1n.

Jacobianadj.2

Jacobianadj.¹n.

Jacobianadj.²