# The Algebra of Invariants (Google eBook)

University Press, 1903 - Forms (Mathematics) - 384 pages

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### Contents

 CHAP PAGE I Introduction 1 The Fundamental Theorem 21 Transvectants 36 Transvectants continued 03 85 Gordans Theorem 101 The Quintic 128 Simultaneous Systems 158 Hilberts Theorem 169
 Ternary Forms 246 Ternary Forms continued 274 Apolarity continued 299 Types op Covariants 319 General Theorems on Quantics 339 The Symbolical Notation 365 Wronskis Theorem 370 Jordans Lemma 375

 Geometry 183 Apolarity and Rational Curves 213
 Types of Covariants 378 Index 381

### Popular passages

Page 270 - Prove that if three binary quadraties ax2, i^2, cx2 are in involution, then (aV) (bc) (ca) = 0 ; deduce the locus of a point such that the tangents from it to three conics form a pencil in involution, and state the correlative theorem.
Page 353 - Let the letters a, , a, , ... an be arranged in any manner in horizontal rows, so that each row has its first letter in the same vertical column, its second letter in a second vertical column, and so on; and so that no row contains more letters than any row above it.
Page 49 - The difference between any two terms of a transvectant is equal to a sum of terms each of which is a term of a transvectant of lower index of forms obtained from the forms in the original transvectant by convolution.
Page 85 - Theorem will be given in the next chapter. For the present we shall content ourselves with...
Page 49 - Theorem. (1) The difference between any two terms of a transvectant is equal to a sum of terms each of which is a term of a transvectant of lower index of forms obtained from the forms in the original transvectant by convolution.
Page 26 - ... ADMISSIBLE WAVE-FUNCTIONS In the preceding section we have been concerned only with wave-functions of the orbital motion, but the analysis is unaltered if P0 and P contain also spin and charge dependence, so we shall now suppose that P0 is a completely antisymmetric expression; it can be written as the sum of a number of terms each of which is the product of a polynomial of degree N in the co-ordinates with a spin-charge function. The case which arises most often is that in which all single-particle...
Page 170 - If a homogeneous function of any number of variables be formed according to any definite laws, then, although there may be an infinite number of functions F satisfying the conditions laid down, nevertheless a finite number Fl, F2, ... Fr can...
Page 14 - Px — • • • 1 be an aggregate of terms each of which is a product of factors of the type (a/3), then / is an invariant of the quantic.
Page 367 - ... 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 of hyperdeterminants. The reader may feel the need of justifying directly the results obtained by manipulating umbral expressions and accordingly we shall indicate...
Page 308 - This method of representing a point by the parameters of the tangents drawn from it to a fixed conic...