Invariants as Products and a Vector Interpretation of the Symbolic Method, ... |
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a₁ adjacent terms algebraic product apply arithmetic mean Ausdehnungslehre binary forms called changes of sign coefficients complex folding product complex product compound folding product compound product consider corresponds cubic defined degree determinants distributive property e,e₂ e₁ e₁e₂ e₂ e₂² e₂e₂ equation Example expansion expressed in terms extensive form extensive fraction f.e₁ f.e₂ f.g h form unit g.e₂ geometric interpretation given Grace and Young Grassmann introduces Hermann Grassmann Hessian invariants and covariants isobaric Jacobian Lemma linear combination linear transformation lower connection mass Müller non-coincident points nth folding product numerical factor omega operator outer product pair of elements parenthesis point elements polar point polyvalent vector products of f Projective Geometrie proof quadratic form quantic reduces to zero regressive product result second folding product second order set of forms simple elements strokes symbolic notation symmetrical matrix terms of lower ternary Theorem theory of invariants ucts δέ
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Page 1 - ... in the coefficients of each of certain q-ary forms can be expressed as a linear function of the coefficients of the concomitants of those forms. APPENDIX I. NOTE ON THE SYMBOLICAL NOTATION. As we have said in § 82 the notation used in this work is really equivalent to Cayley's hyperdeterminants. The great advance made by the German school lies in the possibility of transforming symbolical expressions, and, of course, in the proof that every invariant form can be represented as a combination...
Page 1 - With this method of attack for the difficult problems of the theory of invariants, Clebsch and Gordan proved that every invariant and covariant can be expressed as a sum of symbolic products. By developing relations between symbolic...