In mathematicsthe exterior product or wedge product of vectors is an algebraic incontri olimpici algebra used in geometry to study areasvolumesand their higher-dimensional analogues. One way to visualize a bivector is as a family of parallelograms all lying in the same plane, having the same area, and with the same orientation —a choice of clockwise or counterclockwise. When regarded in this manner, the exterior product of two vectors is called a 2-blade. More generally, the exterior product of any number k of incontri olimpici algebra can be defined and is sometimes called a k -blade. It lives in a space known as the k th exterior power. The magnitude of the resulting k -blade is the volume of the k -dimensional parallelotope whose edges are the given vectors, just as the magnitude of the scalar triple product of vectors in three dimensions gives the volume of the parallelepiped generated by those vectors. The exterior algebraor Grassmann algebra after Hermann Grassmann is the algebraic system whose product is the exterior product. The exterior algebra provides an algebraic setting in which to answer geometric questions. For instance, blades have a concrete geometric interpretation, incontri olimpici algebra objects in the exterior algebra can be manipulated according to a set of unambiguous rules. The exterior algebra contains objects that are not only k -blades, but sums of k -blades; such a sum is called a k -vector. The rank of any k -vector is defined to be the smallest number of simple elements of which it is a sum. The exterior product extends to the full exterior algebra, so that it makes sense to multiply any two elements of the algebra.Navigation menu
It is one of these more general constructions where the exterior algebra finds one of its most important applications, where it appears as the algebra of differential forms that is fundamental in areas that use differential geometry. Let L be a Lie algebra over a field K , then it is possible to define the structure of a chain complex on the exterior algebra of L. Glossary of tensor theory. This is spanned by decomposable tensors. This is thus more general than the result quoted above for direct sums, since not every short exact sequence splits in other abelian categories. Differential forms play a major role in diverse areas of differential geometry. In particular, the dimension of the space of alternating maps from V k to K is n choose k. Kahan , Jordan's normal form. From Wikipedia, the free encyclopedia. Le quattro giornate sono dedicate ai quattro argomenti in cui possono essere suddivisi gli argomenti tipici delle competizioni matematiche: Its six degrees of freedom are identified with the electric and magnetic fields. Kronecker delta Levi-Civita symbol metric tensor nonmetricity tensor Christoffel symbols Ricci curvature Riemann curvature tensor Weyl tensor torsion tensor. Let T r V be the space of homogeneous tensors of degree r.
Esercizi di Algebra Incontri Olimpici - Montecatini Terme Esercizio 1. Sia p(x) un polinomio a coe cienti interi tale che p(1) = 7 e p(7) = 1. Incontri Olimpici Stage per Insegnanti su argomenti di matematica olimpica Dipartimento di Matematica "ebonypornmag.com" - Viale Morgagni 67/A Firenze, Dicembre ALGEBRA Prof. Paolo Gronchi (Università di Firenze) Video Alessandra Caraceni (SNS, Pisa) Video. Gli Incontri Olimpici sono rivolti a docenti della scuola secondaria. Le quattro giornate sono dedicate ai quattro argomenti in cui possono essere suddivisi gli argomenti tipici delle competizioni matematiche: algebra, aritmetica (teoria dei numeri), combinatoria e geometria. Incontri Olimpici Stage per insegnanti su argomenti di matematica olimpica Aemilia Hotel - Bologna Lunedì 14/10 – Tema della giornata: ALGEBRA – Prof. Emanuele Callegari (Univ. di Roma “Tor Vergata”) – Prof. Devit Abriani (Univ. di Urbino).