To find dual basis from the inner product Matrix!? 1. The problem statement, all variables and given/known data WE know the inner product matrix (capital)Gamma and that's all. How do we "construct" a dual basis? 2. Relevant equations 3. The attempt at a solution I know that the orthonormal basis is nothing but a dual basis. and we can constuct orthonormal basis using G-S method. But, I am clueless about how to construct dual basis from Gamma? Thanks in advance.