Free family

See also: Family

In Linear algebra, a free family is a family of Vecteur S linearly independent (see linear Indépendance).

Mathematical definition

A $F\; family\; =\; (f\_1,\; f\_2,\; \backslash \; ldots,\; f\_n)$ of elements of one K vector Space E is known as K-free if and only if:

$\backslash \; forall\; (\backslash \; lambda\_1,\; \backslash \; lambda\; \_2,\dots ,\; \backslash \; lambda\_n)\; \backslash \; in\; K^n,\; \backslash \; \backslash \; sum\_\; \{k=1\}\; ^n\; \backslash \; lambda\_k\; f\_k\; =\; 0\; \backslash \; Longrightarrow\; \backslash \; forall\; K\; \backslash \; in\; \backslash \; \{1,\; \backslash \; ldots,\; N\; \backslash \},\; \backslash \; \backslash \; lambda\_k\; =\; 0$

So in more the family is generating Famille, it is a bases.

See too

• Family (mathematics)

• generating Family
• Base (linear algebra)

Random links:

Frettemeule | George Robert Milne Murray | Etienne Heudelet de Bierre | Tropical depression Eighteen-E (2006) | Continuation of polynomials | Armure_d'intercepteur

© 2007-2008 speedlook.com; article text available under the terms of GFDL, from fr.wikipedia.org