Proceedings of the Royal Society of Edinburgh Volume 21

Proceedings of the Royal Society of Edinburgh Volume 21

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1897 edition. Excerpt: ... the eliminant of a set of quadrics in more than four variables. 3. As an illustration of tho two methods of forming tho eliminant of a set of ternary quadrics consider tho equations ax2+ fyz+ gzx+ hxy = 0 iY + f'!/z+ 9x+ ll = 0 (!) c"z2 + f'yz + j"zx + h"xy = 0' discussed by Sylvester and Muir. Cambridge Mathematical Journal, vol. ii. p. 235. Sue also Muir, History of Determinants, p. 233. t Salmon, Higher Algebra, 90, p. 85. t Lot. eil., p. 233. Proe. Roy. Soc Edin., -vol. xxi. pp. 220 234. the eliminant may also be expressed as 43ab'c" times the determinant aA+/F h'B' + g'(gh"-af) g"C" + h"(g'h-of) hA + f(h"f-b'g") b'B' + g'G' f"C" + h"(h'f-b'g) (4).'/A-e"h') fB' + g'(/g"-c"h) c"C" + h"ll" 6. If with Sylvester and Muir we reject the special factor i3af/c" the eliminant of (1) is the third order determinant (3), or what is the same thing, the third order determinant (4). From (3) it is obvious that when a = V = c" = 0 the eliminant reduces to FG'H" A and from (4) it is obvious that when the eliminant reduces to AB'C'A'. 7. Returning now to the other method of elimination we find, on eliminating J3, X-ij, etc., dialytically from the Jacobian J and the nine equations obtained from (1) by multiplying each equation by x, y, 2, for the eliminant of (1), the determinant This form of the eliminant is equivalent to that given by Muir in the last volume of the Proceedings, p. 233 (). In the special cases considered in 6, all the elements of the last row of (6) except the last vanish. The last element of the last row of (6) reduces to either A or A', and its co-factor reduces to either and more

Product details

  • Paperback | 226 pages
  • 189 x 246 x 12mm | 413g
  • English
  • Illustrations, black and white
  • 1236794966
  • 9781236794963