Source-pinned research
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This index contains 591 research declarations. Search 10,000 more complete Mathlib declarations.
591 results
Clear filtersLinearPMap.IsSymmetric.pointSpectrum_real
Plain-language statement
Eigenvalues of a symmetric unbounded operator are real.
Source project: Physlib
Person-level attribution pending.
LinearPMap.IsSymmetric.regularityDomain_isConnected_iff
Plain-language statement
The regularity domain of a symmetric operator is connected iff it contains a real number.
Source project: Physlib
Person-level attribution pending.
LinearPMap.IsUnbounded.orthogonal_adjoint_sub_ker
Plain-language statement
(T† - conj z • 1).kerᗮ = (T.closure - z • 1).range
Source project: Physlib
Person-level attribution pending.
LinearPMap.IsUnbounded.orthogonal_closure_sub_range
Plain-language statement
(T.closure - z • 1).rangeᗮ = (T† - conj z • 1).ker
Source project: Physlib
Person-level attribution pending.
LinearPMap.mem_regularityDomain_iff
Plain-language statement
z is a regular point for T iff T - z • 1 has a continuous (equivalently, bounded) inverse.
Source project: Physlib
Person-level attribution pending.
LinearPMap.numericalRange_convex
Project documentation
The Toeplitz-Hausdorff theorem.
Source project: Physlib
Person-level attribution pending.