Origin of Jacobian

after Karl G. J.*Jakobi*(1804-51), German mathematician

Math. a determinant whose elements are the first, partial derivatives of a finite number of functions of the same number of variables, with the elements in each row being the derivatives of the same function with respect to each of the variables

Origin of Jacobian

after Karl G. J.Webster's New World College Dictionary, Fifth Edition Copyright © 2014 by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

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**MLA Style**

"Jacobian." YourDictionary, n.d. Web. 21 January 2019. <https://www.yourdictionary.com/Jacobian>.

**APA Style**

Jacobian. (n.d.). Retrieved January 21st, 2019, from https://www.yourdictionary.com/Jacobian

Adjective

(*not comparable*)

- Alternative capitalization of
*Jacobian*.

Noun

(*plural* jacobians)

- Alternative capitalization of
*Jacobian*.

English Wiktionary. Available under CC-BY-SA license.

Link to this page

Cite this page

**MLA Style**

"Jacobian." YourDictionary, n.d. Web. 21 January 2019. <https://www.yourdictionary.com/Jacobian>.

**APA Style**

Jacobian. (n.d.). Retrieved January 21st, 2019, from https://www.yourdictionary.com/Jacobian

- We can prove that if the three equations be satisfied by a system of values of the variable, the same system will also satisfy the
**Jacobian**or functional determinant. - For if u, v, w be the polynomials of orders m, n, p respectively, the
**Jacobian**is (u 1 v 2 w3), and by Euler's theorem of homogeneous functions xu i +yu 2 +zu 3 = mu xv1 +yv2 +zv3 = /IV xw 1+y w 2+ zw 3 = pw; denoting now the reciprocal determinant by (U 1 V2 W3) we obtain Jx =muUi+nvVi+pwWi; Jy=ï¿½.., Jz=..., and it appears that the vanishing of u, v, and w implies the vanishing of J. - CY The proof being of general application we may state that a system of values which causes the vanishing of k polynomials in k variables causes also the vanishing of the
**Jacobian**, and in particular, when the forms are of the same degree, the vanishing also of the differential coefficients of the**Jacobian**in regard to each of the variables. - Since, If F = An, 4) = By, 1 = I (Df A4) Of A?) Ab A"'^1Bz 1=, (F, Mn Ax I Ax 2 Axe Ax1) J The First Transvectant Differs But By A Numerical Factor From The
**Jacobian**Or Functional Determinant, Of The Two Forms. We Can Find An Expression For The First Transvectant Of (F, ï¿½) 1 Over Another Form Cp. For (M N)(F,4)), =Nf.4Y Mfy.4), And F,4, F 5.4)= (Axby A Y B X) A X B X 1= (Xy)(F,4))1; (F,Ct)1=F5.D' 7,(Xy)(F4)1. - Solving the equation by the Ordinary Theory Of Linear Partial Differential Equations, We Obtain P Q 1 Independent Solutions, Of Which P Appertain To S2Au = 0, Q To 12 B U =0; The Remaining One Is Ab =Aobl A 1 Bo, The Leading Coefficient Of The
**Jacobian**Of The Two Forms. This Constitutes An Algebraically Complete System, And, In Terms Of Its Members, All Seminvariants Can Be Rationally Expressed.

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