Skip to content

feat: prove Schur product theorem (IsPositiveDefinite.mul)#2

Merged
slink merged 1 commit intomainfrom
worktree-agent-ac6e488f
Mar 1, 2026
Merged

feat: prove Schur product theorem (IsPositiveDefinite.mul)#2
slink merged 1 commit intomainfrom
worktree-agent-ac6e488f

Conversation

@slink
Copy link
Owner

@slink slink commented Mar 1, 2026

Summary

  • Strengthen IsPositiveDefinite definition from .re >= 0 to complex nonneg (real AND nonneg)
  • Prove Schur product theorem (mul) via spectral decomposition of PSD kernel matrix
  • Prove Hermitian symmetry (conj_neg), matrix bridge (pdMatrix_posSemidef), convenience accessors
  • Update closure_pointwise and of_charFun for strengthened definition
  • Zero sorries remaining in PositiveDefinite.lean

Sorry audit

  • No sorries in PositiveDefinite.lean (was 1, now 0)

Test plan

  • lake build succeeds (full project, 6254 jobs)
  • Zero sorries in PositiveDefinite.lean
  • All downstream files compile unchanged

Strengthen IsPositiveDefinite definition to require complex nonneg
(both .re >= 0 AND .im = 0) matching standard probability theory
references. Prove the Schur product theorem: pointwise product of PD
functions is PD, via spectral decomposition of the PSD kernel matrix.

New lemmas: re_nonneg, im_eq_zero, apply_zero_im, conj_neg,
pdMatrix_posSemidef. Updates closure_pointwise and of_charFun for
the strengthened definition.
@slink slink merged commit 2a1ba1c into main Mar 1, 2026
2 checks passed
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment

Labels

None yet

Projects

None yet

Development

Successfully merging this pull request may close these issues.

1 participant