منابع مشابه
Classification of trilinear operations
We use the representation theory of the symmetric group to classify up to equivalence all multilinear operations over the field Q of rational numbers. In the case n = 3, we obtain explicit representatives of the equivalence classes of trilinear operations [a, b, c] = x1 abc + x2 acb + x3 bac + x4 bca + x5 cab + x6 cba (xi ∈ Q). From these results we obtain one-parameter families of deformations...
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Let T : H1 H2 H3 ! C be a trilinear form where H1, H2, H3 are separable Hilbertspaces. In the hypothesis that at least two of the three spaces are nite dimensional weshow that the norm square = kTk2 is a root of a certain algebraic equation, usually ofvery high degree, which we baptize the milleniar equation, because it is an analogue ofthe secular equation in the bilinear c...
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We study the triangle bounded by the antiparallels to the sidelines of a given triangle ABC through the intercepts of the trilinear polar of a point P other than the centroid G. We show that this triangle is perspective with the reference triangle, and also study the condition of concurrency of the antiparallels. Finally, we also study the configuration of induced GP -lines and obtain an intere...
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Dear friends, In 1997 or 1998 I began to write a paper [20], trying to extend the known description of binary forms of norm unity, in the real or complex cases, to the case of quaternions, but I never finished it. In 2002, I resumed my work but then I was unable to understand what I had done, so I made a fresh start with somewhat different assumptions. Now I have realized that this was a gross ...
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ژورنال
عنوان ژورنال: Physics Today
سال: 1957
ISSN: 0031-9228,1945-0699
DOI: 10.1063/1.3060142