I don't really get what this matrix looks like. From what I have been reading w are integer vectors, just like v, but the dot product of these vectors isn't another vector so what does this matrix look like? And how does that just get me (V^T)^(-1)? Is it because the entries of V are just integers as well, and since it is a basis for L I am just getting linear combinations of the basis? I have a feeling my questions and comments are pretty naive but I just don't see it and I really want to understand. I always do better when I can play with the math, but I can't play with a definition and this isn't in our text. Thank you for taking the time to explain some of this to me.