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Circular vectors and toroidal matrices

Znojil, M. (1996)

Proceedings of the Winter School "Geometry and Physics"

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.

Clifford algebra with Reduce

Brackx, Freddy, Constales, Denis, Delanghe, Richard, Serras, Herman (1987)

Proceedings of the Winter School "Geometry and Physics"

Clifford approach to metric manifolds

Chisholm, J. S. R., Farwell, R. S. (1991)

Proceedings of the Winter School "Geometry and Physics"

[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 { e j : j = 1 , , n } satisfying the condition { e i , e j } e i e j = e j e i = 2 I η i j , where I denotes the unit scalar of the algebra and ( η i j ) the nonsingular Minkowski...

Co je dobrá matematika?

Terrence Tao (2008)

Pokroky matematiky, fyziky a astronomie

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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