Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 63 / 1 / Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 4 / 8E / b / Solution

For a symmetric bilinear form $B$, the same projection formula
$$
u_k=v_k-\sum_{j<k}\frac{B(v_k,u_j)}{B(u_j,u_j)}u_j
$$
produces a $B$-orthogonal basis whenever the chosen pivots $B(u_j,u_j)$ are nonzero. Reordering the input vectors can avoid a zero pivot when a suitable anisotropic vector remains.

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 Incoming links: Gram-Schmidt orthogonalization for a symmetric bilinear form