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I am not really sure how to translate "E spans F" into french. Could some of the french users assist me ?

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Judging by the article on vector spaces in French Wikipedia, $E$ engendre $F$, and $F$ is engendré par (la famille) $E$. – Brian M. Scott Sep 16 '13 at 20:37
I agree : "$E$ engendre $F$". – Etienne Sep 16 '13 at 20:40
Remark: If we have a set $(x_i)_{i\in I}$ of vectors that spans a vector space $E$ then the symbolic translation of $E=\mathrm{span}(x_i)$ is $E=\mathrm{vect}(x_i)$ – user63181 Sep 16 '13 at 20:52
up vote 4 down vote accepted

$E$ engendre $F$, or, la famille $E$ engendre $F$ and its declinations $F$ est engendrée par $E$ or l'espace vectoriel $F$ est engendré par $E$.

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