Source-pinned research

Research proof index

Search theorem names, mathematical ideas, modules, topics, projects, and role-labelled researchers. Open a result for its complete indexed Lean declaration and source record.

This index contains 3 research declarations. Search 10,000 more complete Mathlib declarations.

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Project-declaredLean 4.32.0

Variance eq norm sq sub expected Value sq

LinearPMap.variance_eq_norm_sq_sub_expectedValue_sq

Plain-language statement

For symmetric T and ‖ψ‖ = 1, variance equals ‖Tψ‖ ^ 2 - ⟨T⟩_ψ ^ 2.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Variance eq zero iff is Eigenvector

LinearPMap.variance_eq_zero_iff_isEigenvector

Plain-language statement

For ‖ψ‖ = 1, zero variance iff ψ is an eigenvector with eigenvalue ⟨T⟩_ψ.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

View proof record