TY - JOUR
AU - Turnbull, H. W.
AB - TWO QUADRATIC FORMS IN 71 VARIABLES. 469 ON THE COMPLETE SYSTEM OF TWO QUADRATIC FORMS IN u VARIABLES. By H. W. TURNBULL. [Received 21 March, 1929.—Read 25 April, 1929.] 1. Introduction. The following pages deal with the complete system of concomitants of two quadratic forms in n variables : F = XaijXiXj, F' = ZrjjXiXj. According" to Gordon's theorem, the irreducible concomitants are finite in number. Such a finite system, inclusive, with possible redundancies, of all irreducibles, I gave twenty years ago*. In the work, which involved an intricate argument, it was pointed out (page 239) that the results could be simplified by resolving each variable x, or cogredient variable y, into n—1 variables u, v, w, ..., each contragredient to x, and then treating the problem for coefficients a^, r and variables u v ..., alone. In !} it ti the present work this has been done, and the system has been estab- lished by what seems to be an essentially simplified form of the original method. The system first given was unsymmetrical, but the result here obtained is perfectly symmetrical in the ground forms. This system agrees with, the known binary and ternary cases (loc. cit., page 
TI - On the Complete Systems of two Quadratic Forms in n Variables
JF - Proceedings of the London Mathematical Society
DO - 10.1112/plms/s2-30.1.469
DA - 1930-01-01
UR - https://www.deepdyve.com/lp/wiley/on-the-complete-systems-of-two-quadratic-forms-in-n-variables-skjdYRUTl1
SP - 469
EP - 480
VL - s2-30
IS - 1
DP - DeepDyve
ER -