Sentence Examples

  • It will be observed that in the first process the value of the modulus is in fact calculated from the formula.
  • By solving the equations of transformation we obtain rE1 = a22x1 - a12x1, r = - a21x1 + allx2, aua12 where r = I = anon-anon; a21 a22 r is termed the determinant of substitution or modulus of transformation; we assure x 1, x 2 to be independents, so that r must differ from zero.
  • In the theory of forms we seek functions of the coefficients and variables of the original quantic which, save as to a power of the modulus of transformation, are equal to the like functions of the coefficients and variables of the transformed quantic. We may have such a function which does not involve the variables, viz.
  • For the substitution rr xl =A 11 +1 2 12, 52=A21+�2E2, of modulus A1 �i = (Al�.2-A2�1) = (AM), A 2 �2 the quadratic form a k xi -1-2a 1 x i x 2 +a 2 4 = x =f (x), becomes A41 +2A1E16 =At = OW, where Ao = aoA i +2a1AiA2 +a2Az, _ _ A 1 = ao A l�l +ai(A1/.22+A2�1) +7,2X2/22, A2 = ao�l +2a1�1/�2 +a 2�2 � We pass to the symbolic forms a:= (aixi+a2x2) 2, A 2 = (A 151+ A 26) 2/ by writing for ao, al, a2 the symbols ai, a 1 a 2, a?
  • = (A11+A22)n by the substitutions 51 = A l, E1+�1 2, 52 = A2E1+�2E2, the umbrae Al, A2 are expressed in terms of the umbrae al, a 2 by the formulae A l = Alai +A2a2, A2 = �la1 +�2a2� We gather that A1, A2 are transformed to a l, a 2 in such wise that the determinant of transformation reads by rows as the original determinant reads by columns, and that the modulus of the transformation is, as before, (A / .c).