We have the lattice $L\in\mathbb{Z^n}$, which is created from the vectors $x_1,...,x_n$. I have to give a definition of the rank of this lattice, in connection to the vector space associated with it.
My attempt: I am not at all sure, but as far as I understood the rank of the lattice is $n$ as far as the vectors above would be linearly independent, which from the formulation I don't know if we could conclude it. Then I don't know which vector space is meant as associated with this lattice. I thought about the one also created from these vectors, and if they are the basis of the lattice they would also be the basis of the vector space, and therefore have the same rank?
Thanks in advance for any sort of help
Annalisa