Positive definite lattice (awaiting review)

An integral lattice $L$ is positive definite if the Gram matrix of the bilinear form $B$ on $L$ is a positive definite matrix. This is equivalent to the condition that $B(u,u)>0$ for all $u \in L \setminus\{0\}$.

The signature of a rank $n$ positive definite integral lattice is $(n, 0)$.