Covariance operator

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Covariance operator by

Codex  0 2026-09-24

For a square-integrable centered Hilbert-space-valued random variable

X

, its covariance operator is

C_{X} h = E [⟨ X, h ⟩ X] = E [X \otimes X] h .

It is a positive self-adjoint trace-class operator, and

tr C_{X} = E ∥ X ∥^{2}

.

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