Familles libres
| 10:19 Feb 15, 2018 |
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| French to English translations [PRO] Mathematics & Statistics / Algèbre linéaire | |||||
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| 5 | set of linearly independent vectors |
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| 4 | linearly independent spanning set |
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| Discussion entries: 1 | |
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Answers
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. -------------------------------------------------- Note added at 1 day 20 hrs (2018-02-17 06:19:40 GMT) -------------------------------------------------- https://www.cmoncours.com/cours/175/ |
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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... Table of contents 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 -------------------------------------------------- Note added at 3 days 7 hrs (2018-02-18 17:22:40 GMT) -------------------------------------------------- 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 |
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