0

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?

Paulo
  • 1
  • 1
  • There's a confusion here: You have just some inner product, while the thread you're linking is talking about the dot product on $\mathbb{R}^n$. So you need to first choose an orthonormal basis for your inner product and work in that basis. – darij grinberg Feb 12 '19 at 21:51
  • Yes, I understand that, but I was thinking of understanding the euclidian case first and see if it would give me some insight on the general case. – Paulo Feb 12 '19 at 23:34

0 Answers0