The theory of determinants in the historical order of development, by Sir Thomas Muir.

JACOBIANS (NEUMANN, 1868) 263 NEUMANN, C. (1868). [Zur Theorie der Functionaldeterminanten. Math. Annalen, i. pp. 208-209.] This is merely an unexpected verification of Jacobi's 'fundamental lemma' of 1844 (Hist., ii. pp. 230-234). CLEBSCH, A. (1868). [Ueber eine Eigenschaft von Functionaldeterminanten. Crelle's Journ., lxix. pp. 355-358.] [Note zu dem Aufsatze "Ueber eine Eigenschaft...." Crelle's Journ., lxx. pp. 175-181.] The property in question is to the effect that If uP, u2,?3u.... be n +1I homogeneous integral functions of the rt1 degree in the n variables x1, x,,,...; v1, v2,..., v,,,l be the set of Jacobians formed from the u's; and wl, w,..., w,,+ the set formed in like manner from the v's; then u U2= U3 Wi W2 W3 By way of proof it is shown that, whatever values the a's and b's may have, the last row of the determinant av,?V,. x a a, b, yax, aDy ODy2 ax, ax... ax, a b2,av- a?n+ avn, ~a Dx3-1 Dx2 D laayj, i~b,,Uh can be made to vanish: that therefore Eb,hu, -Ea,w, - Zahuh.Zbkwk = 0; and that therefore, "by putting the coefficients of the products akb, separately equal to zero," there results UhW7 - Ukwh, = 0 as desired.

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Title
The theory of determinants in the historical order of development, by Sir Thomas Muir.
Author
Muir, Thomas, Sir, 1844-1934.
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Page 252
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London,: Macmillan and Co., Limited,
1906-
Subject terms
Determinants

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"The theory of determinants in the historical order of development, by Sir Thomas Muir." In the digital collection University of Michigan Historical Math Collection. https://name.umdl.umich.edu/acm9350.0003.001. University of Michigan Library Digital Collections. Accessed May 29, 2025.
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