I was working on this problem:
Let L be a n dimensional vector space, g a inner product on L. Show that {$e_1,...,e_n$} is linearly independent iff the matrix $G=(g(e_i,e_j))$ is non singular.
I wasnt able to solve it, and found this: Gram matrix invertible iff set of vectors linearly independent
I do understand the argument, except for the part where it's affirmed that $G=A^TA$.
I feel like I'm missing something obvious here, but I just can't see it. Could someone give me some insight?