# Familles libres

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 10:19 Feb 15, 2018

French to English translations [PRO]
Mathematics & Statistics / Algèbre linéaire
 French term or phrase: Familles libres Algèbre 2 Etudier l'algèbre linéaire Espaces vectoriels, sous-espaces, somme direct. ///////Familles libres,/////// familles génératrices, bases, théorème de la base incomplète. Dimension. From document describing the courses for a Bachelor's degree "licence de sciences, technologies, santé - Mention mathématiques" Thanks for your help with reference if possible.
 Ghyslaine LE NAGARDNew Caledonia Local time: 16:17

5set of linearly independent vectors
 Francois Boye
4linearly independent spanning set
 herbalchemist

Discussion entries: 1

5 hrs   confidence:
set of linearly independent vectors

Explanation:
Linearly independent vectors

Vector c is a linear combination of vectors a and b, because c = a + b. Therefore, the set of vectors a, b, and c is linearly dependent. Vectors d, e, and f are linearly independent, since no vector in the set can be derived as a scalar multiple or a linear combination of any other vectors in the set.

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Note added at 1 day 20 hrs (2018-02-17 06:19:40 GMT)
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https://www.cmoncours.com/cours/175/

 Francois BoyeUnited StatesLocal time: 01:17Specializes in fieldNative speaker of: FrenchPRO pts in category: 4

neutral  philgoddard: I have no idea whether this is correct, but your "explanation" is lifted from someone else's website.
 22 mins
-> This is the definition of linear algebra they teach all over the world

2 days 23 hrs   confidence:
Famille libre
linearly independent spanning set

Explanation:
For your list, "linear independence" should work as well.

https://fr.wikipedia.org/wiki/Indépendance_linéaire
En algèbre linéaire, étant donnée une famille de vecteurs d'un même espace vectoriel, les vecteurs de la famille sont linéairement indépendants, ou forment une famille libre, si la seule combinaison linéaire de ces vecteurs qui soit égale au vecteur nul est celle dont tous les coefficients sont nuls.

http://linear.ups.edu/html/section-LISS.html
This is a very typical use of the hypothesis that a set is linearly independent — obtain a relation of linear dependence and then conclude that the scalars must all be zero. The result of this theorem tells us that we can write any vector in a vector space as a linear combination of the vectors in a linearly independent spanning set, but only just. There is only enough raw material in the spanning set to write each vector one way as a linear combination. So in this sense, we could call a linearly independent spanning set a “minimal spanning set.” These sets are so important that we will give them a simpler name (“basis”) and explore their properties further in the next section.

https://www.ma.utexas.edu/users/rav/M341.Summer13/M341.Basis...
1 Span, linear independence, basis and dimension
1.1 Span
1.1.1 Computing span in Rm
1.1.2 Minimal spanning subset
1.2 Linear independence
1.2.1 Determining linear independence in Rm
1.2.2 Maximal linearly independent subset
1.3 Basis and dimension
1.3.1 Definitions and basic results
1.3.2 Constructing bases from spanning sets and linearly independent sets
1.3.3 Dimension of a subspace

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Note added at 3 days 7 hrs (2018-02-18 17:22:40 GMT)
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Edit:
-famille libre is linearly independent set
-famille génératrice is spanning set
-base is basis = linearly independent spanning set
You could use family, but we did not in the Linear Algebra course I took.
http://www.maths.qmul.ac.uk/~pjc/comb/matroid.pdf

 herbalchemistGermanyLocal time: 07:17Native speaker of: English

neutral  Francois Boye: You have confirmed the concept of 'linear independence of vectors'. So why do you reject?
 2 days 5 hrs

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