We have a subset $A$ inside a vectorial space $E$.
We call $Vect(A)$ the smallest vectorial space containing $A$ included in $E$.
I defined it as $Vect(A)=\{x ~/ x=\lambda a, \lambda \in \mathbb{K}, a \in A \}$
But it doesn't work if $A=\varnothing$
My question is thus :
Is my definition true for any other part than $\varnothing$ or there is something wrong in what I wrote ? (Is the case $\varnothing$ the only exception where my definition isn't true).