Question

State and prove that the Bessel’s Inequality for finite dimensional inner product space.​

Answer 1

We now use the Pythagorean identity to prove the very important Bessel's inequality. Lemma 1: Let be an inner product space. ... If $\{ e_1, e_2, ..., e_n \}$ is an orthonormal set then for all , $\displaystyle{\sum_{k=1}^{n} \langle e_k, h \rangle^2 \leq \| h \|^2}$.

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