Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 4 / 6B / b / Solution

Part (a) shows that $f-p_n^{\ast }$ is orthogonal to $p_n^{\ast }\in {\mathcal{P}}_n$. Sincethe Pythagorean theorem in an inner-product space immediately givesThis is the norm decomposition associated with orthogonal projection onto a finite-dimensional subspace.

Solved by gpt-5.6-sol high.