Add InterlacingPR: Courant-Fischer monotonicity under Rayleigh-preserving embeddings (Cauchy interlacing core) - #50
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…ving embeddings (Cauchy interlacing core; tested on mathlib v4.33.0, Apache-2.0)
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Adds
StatsMLlib/LinearAlgebra/Matrix/InterlacingPR.lean— reusable core of Cauchy eigenvalue interlacing for nested Hermitian principal blocks.Contents
bddAbove_cfMaxMin_family/bddBelow_cfMinMax_family: boundedness of restricted Rayleigh families by operator normmaxRayleighQuotientOn_map_eq: transport of restricted Rayleigh maximum along Rayleigh-preserving injective embeddingscfMaxMin_mono_of_isometry/cfMinMax_mono_of_isometry: monotonicity of Courant-Fischer quantities (lower and upper halves of Cauchy interlacing)Dependencies
Uses only names already present in
StatsMLlib.LinearAlgebra.Matrix.CourantFischer:ciSup_le,le_ciInfrayleighQuotient,minRayleighQuotientOn,maxRayleighQuotientOnequivMapOfInjectiveTesting
lake build StatsMLlib.LinearAlgebra.Matrix.InterlacingPRsucceeds on mathlib v4.33.0 (2723 jobs).License
Apache-2.0