Hilbertian basis

A Hilbertian basis is a complete orthonormal family: its closed linear span is the whole Hilbert space, equivalently every vector is the norm-convergent sum of its Fourier coefficients against the basis.

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- Parseval identity for a Hilbertian basis Hilbertian basis

Parseval identity for a Hilbertian basis

For a Hilbertian basis

(e_{i})

,

⟨ x, y ⟩ = \sum_{i} ⟨ x, e_{i} ⟩ \overline{⟨ y, e_{i} ⟩}, ∥ x ∥^{2} = \sum_{i} ∣ ⟨ x, e_{i} ⟩ ∣^{2} .

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Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 5 / 2 / 3 / Solution
Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 1 / 22H / a / ii / Solution
Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 2 / 22G / b / Solution
Separable Hilbert space

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