proving there exist another basis of non-degenerate quadratic space (V,B) other than the given basis

29 Views Asked by At

If {$v_i$} is a basis of non-degenerate quadratic space ($V,B$) (finite),

prove that there exists another basis {$w_i$} such that

$$B(v_i,w_j)=1 (i=j)$$ $$or 0(i \neq j)$$

Sorry for the ugly text styling, I don't know how to use them very well.

I am stuck from the very beginning, can anyone help me?