Sentence Examples

  • Also such ideas as those of invariants, groups and of form, have modified the entire science.
  • The partition method of treating symmetrical algebra is one which has been singularly successful in indicating new paths of advance in the theory of invariants; the important theorem of expressibility is, directly we exclude unity from the partitions, a theorem concerning the expressibility of covariants, and involves the theory of the reducible forms and of the syzygies.
  • For example, the theory of invariants may be regarded as depending upon the consideration of the symmetric functions of the differences of the roots of the equation aox n - (i) a i x n - 1 + (z) a 2 x n 2 - ...
  • The important result is that the theory of invariants is from a certain point of view coincident with the theory of non-unitary symmetric functions.
  • An important notion in the theory of linear operators in general is that of MacMahon's multilinear operator (" Theory of a Multilinear partial Differential Operator with Applications to the Theories of Invariants and Reciprocants," Proc. Lond.

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