Let $f$ be a symmetric bilinear form.Let $\{\alpha_1,...,\alpha_n\}$ be a basis.Now we know that we can find an orthogonal basis by Gram Schmidt process which is as follows:
$\beta_1=\alpha_1$ and $\beta_n=\alpha_n-\sum\limits_{j=1}^{n-1}\frac{f(\alpha_n,\beta_j)}{f(\beta_j,\beta_j)}\beta_j$.But what happens if $f(\beta_j,\beta_j)=0$ for some $j$.
Should we modify this process in order to avoid such situation?Can someone give me a basis where such situation arises?