Multivektor

Polivektor (tudi multivektor ali p-vektor) je v multilinearni algebri element, ki pripada zunanji algebri nad vektorskim prostorom. To algebro sestavljajo linearne kombinacije enostavnih k-vektorjev

${\displaystyle v_{1}\wedge \cdots \wedge v_{k}.}$

Zunanjo potenco stopnje k označimo z

${\displaystyle \Lambda ^{k}(V),}$.

Produkt k-multivektorja in ${\displaystyle \ell }$-multivektorja je ${\displaystyle (k+\ell )}$-multivektor.

V diferencialni geometriji je p-vektor tenzor, ki se dobi kot zunanji produkt p tangentnih vektorjev. Pri tem pa je ${\displaystyle p>1\,}$. To je zamisel, ki izhaja iz dualnega prostora za p-formo.

Kadar je ${\displaystyle p=2\,}$ dobimo bivektor. Če pa je ${\displaystyle p=3\,}$, dobimo trivektor. So dualni z 2 formo (bilinearna forma) in 3 formo ^[1][2]

1. ↑ William M Pezzaglia Jr. (1992). »Clifford algebra derivation of the characteristic hypersurfaces of Maxwell's equations«. V Julian Ławrynowicz (ur.). Deformations of mathematical structures II. Springer. str. 131 ff. ISBN 0792325761. Hence in 3D we associate the alternate terms of pseudovector for bivector, and pseudoscalar for the trivector
2. ↑ Baylis (1994). Theoretical methods in the physical sciences: an introduction to problem solving using Maple V. Birkhäuser. str. 234, see footnote. ISBN 081763715X.