# Incontri olimpici algebra

In mathematicsthe exterior product or wedge product of vectors is an algebraic construction 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 **incontri olimpici algebra.** More generally, the exterior product of any number k of vectors can be defined and is sometimes called a k -blade. It lives in a incontri cassno 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[4] is the algebraic system whose product is the exterior product. The *incontri olimpici algebra* algebra provides an algebraic setting in which to answer geometric questions. For instance, blades have a concrete geometric interpretation, and objects in the exterior algebra can be manipulated according to a set of unambiguous rules. The exterior algebra contains objects that **incontri olimpici algebra** not only k -blades, but sums of k -blades; such a sum is called a k -vector. The rank of any k -vector is incontri massaggi a latina to be the smallest number of simple elements of which it is a sum.

By using this site, you agree to the Terms of Use and Privacy Policy. In applications to linear algebra , the exterior product provides an abstract algebraic manner for describing the determinant and the minors of a matrix. Suppose that V and W are a pair of vector spaces and f: Precedente Risultati delle Olimpiadi Internazionali di Matematica More generally, the exterior product of any number k of vectors can be defined and is sometimes called a k -blade. In this case an alternating multilinear function. A short while later, Alfred North Whitehead , borrowing from the ideas of Peano and Grassmann, introduced his universal algebra. These ideas can be extended not just to matrices but to linear transformations as well: 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. The import of this new theory of vectors and multivectors was lost to mid 19th century mathematicians, [25] until being thoroughly vetted by Giuseppe Peano in The exterior algebra also has many algebraic properties that make it a convenient tool in algebra itself. Views Read Edit View history. See the article on tensor algebras for a detailed treatment of the topic.

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 "alosangeleslove.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).