feat: add Lidskii–Last eigenvalue-perturbation eval problem#274
Open
kim-em wants to merge 1 commit into
Open
Conversation
This PR adds the Lidskii-Last theorem (§99 of Knill's "Some Fundamental Theorems in Mathematics") as a new eval problem: for self-adjoint complex matrices A, B with eigenvalues sorted in the same order, the total eigenvalue displacement is bounded by the entrywise ℓ¹ distance. Mathlib has no Lidskii, Ky Fan, or Hoffman-Wielandt perturbation bounds. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
1 participant
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
This PR adds the Lidskii–Last eigenvalue-perturbation theorem as a new lean-eval challenge problem — §99 of Oliver Knill's Some Fundamental Theorems in Mathematics.
For two self-adjoint complex
n × nmatricesA, Bwith eigenvalues sorted in the same order, the total eigenvalue displacement is bounded by the entrywiseℓ¹distance:∑ⱼ |αⱼ − βⱼ| ≤ ∑ᵢⱼ |Aᵢⱼ − Bᵢⱼ|.This is Last's theorem (≈1993), a consequence of Lidskii's inequality (1950). The statement uses
Matrix.IsHermitian.eigenvalues₀and needs no auxiliary definitions; mathlib has no Lidskii, Ky Fan, or Hoffman–Wielandt perturbation bounds, and a search found no formalization of the theorem in any other proof assistant.🤖 Prepared with Claude Code