Sentence Examples

  • Now a11A11= alla22a33...ann, wherein all is not to be changed, but the second suffixes in the product a 22 a 33 ...a nn assume all permutations, the number of transpositions necessary determining the sign to be affixed to the member.
  • From the theorem given above for the expansion of a determinant as a sum of products of pairs of corresponding determinants it will be plain that the product of A= (a ll, a22, ��� ann) and D = (b21, b 22, b nn) may be written as a determinant of order 2n, viz.
  • Anibll +an2b12+� �� +annbin a11b21+a12b22+��� +alnb2n, a21b21+a22b22+��� +a2nb2n, � � � ani b21 + a n2 b 22 + � � � +annb2n alib31+a12b32+���+ainb3n, a21b31+a22b32+���+a2nb3n, .�.a n lb 31 + a n2 b 32+ ��� +annb2n a ll b nl + a 12 b n2+ ��� + a ln b nn, a21bn1+a22bn2+�-�+a2nbnn, � � � ani b nl + a n2 b n2 +� � � +annbnn and all the elements of D become zero.
  • In particular the square of a determinant is a deter minant of the same order (b 11 b 22 b 33 ...b nn) such that bik = b ki; it is for this reason termed symmetrical.
  • The Adjoint or Reciprocal Determinant arises from A = (a11a22a33 ...a nn) by substituting for each element A ik the corresponding minor Aik so as to form D = (A 11 A 22 A 33 ��� A nn).