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单词 Parseval's identity
释义

Parseval's identity

The identity states that

for a orthonormal basis x1, x2, …, xn of a finite-dimensional inner product space X and x∈X. This is a generalization of Pythagoras' Theorem. The identity holds for an orthonormal sequence in an infinite-dimensional Hilbert space if and only if the sequence is complete, or equivalently, a Schauder basis. Compare Bessel's inequality.

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更新时间:2025/4/29 11:22:31