Sentence Examples


  • X n/ yl, Y2,...y n j ' x 1, � Forming the product of the first two by the product theorem, we obtain for the element in the ith row and kth column aZ, ayl az i ayz azi ayn ayl + e +...+ where or as a21 a22 ���a2,i -1 a2,i +1 .��a2n a31 ���a3,i -1 a3,ti+ 1 ���a3n ���yi -)tin,and a7,2 ���a,,,i -1 an,i+1 ...an�' a21 a22 ���a2, -1 a32 -1 I.
  • X n/ yl, Y2,...y n j ' x 1, � Forming the product of the first two by the product theorem, we obtain for the element in the ith row and kth column aZ, ayl az i ayz azi ayn ayl + e +...+ where or as a21 a22 ���a2,i -1 a2,i +1 .��a2n a31 ���a3,i -1 a3,ti+ 1 ���a3n ���yi -)tin,and a7,2 ���a,,,i -1 an,i+1 ...an�' a21 a22 ���a2, -1 a32 -1 I.
  • May be a simultaneous invariant of a number of different forms az', bx 2, cx 3, ..., where n1, n 2, n3, ...
  • 1 -az 74 - 2.1 -azn-4....1 - azn+4.1 - az n+2.1 - az-n in which we have to take the coefficient of aezne-2', the expansion.
  • Denominator factors, that the complete system of the quadratic is composed of the form itself of degree order I, 2 shown by az 2, and of the Hessian of degree order 2, o shown by a2.
 

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