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Summary: Arrays of numbers may be written not only on a line (= ``a vector'') or in the plain (= ``a matrix'') but also on a circle (= ``a circular vector''), on a torus (= ``a toroidal matrix'') etc. In the latter case, the immanent index-rotation ambiguity converts the standard ``scalar'' product into a binary operation with several interesting properties.
[For the entire collection see Zbl 0742.00067.]For the purpose of providing a comprehensive model for the physical world, the authors set up the notion of a Clifford manifold which, as mentioned below, admits the usual tensor structure and at the same time a spin structure. One considers the spin space generated by a Clifford algebra, namely, the vector space spanned by an orthonormal basis satisfying the condition , where denotes the unit scalar of the algebra and () the nonsingular Minkowski...
Článek přináší některé mé osobní myšlenky a názory na to, co je dobrá
matematika, a zda bychom se měli snažit definovat tento pojem přesněji. Jako příklad je uveden příběh Szemerédiovy věty.
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