The Kansas University Science Bulletin Volume 6, No. 1

The Kansas University Science Bulletin Volume 6, No. 1

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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. 1911 edition. Excerpt: ... V. We must now return to the consideration of the equations fr = li among the elements of M, which define a system of collineations within Gs having the first group property; and we shall apply the results of Theorem 9 to these equations. Let the three sets of cogredient variables be respectively the elements of the three rows of the matrix Mt let B, etc., ) be a complete family of automorphic forms in the elements of the rows of Mt and let pi be transformed by U. Since the matrix of U is the conjugate of the matrix of M, the coefficients of each of the transformed forms /, will reproduce in the elements of the rows of M the original forms in the rows of Mt. Equating corresponding coefficients of the original and transformed forms we have a set of equations fc(tt b etc., ) =lt which satisfies both conditions of Art. 185. We may let our three sets of cogredient variables be respectively the elements of the three columns of M.; if the complete family of automorphic forms in the elements of these columns be transformed by V, the coefficients of each of the transformed forms will reproduce in the elements of the columns of M, the original forms. Equating as before corresponding coefficients of the original and the transformed forms we have a set of equations fc(a ut, etc, ) = li which satisfies both conditions of Art. 185. We are now able to restate Theorem 8 in a more precise form, thus: THEOREM 8a. The set of equations fi =k on the elements of the matrix Af, which defines a system of collineations within Gs having the fii'st group property, consists of a complete family of automorphic forms in the elements of the rows or columns of Af. each member of the family equated to the corresponding coefficient of the...show more

Product details

  • Paperback
  • 189 x 246 x 4mm | 168g
  • Rarebooksclub.com
  • United States
  • English
  • black & white illustrations
  • 1236803574
  • 9781236803573