feat: add Lidskii's inequality eval problem#291
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This PR adds Lidskii's inequality (§99 of Knill's "Some Fundamental Theorems in Mathematics", an additional statement of the section; the boxed main theorem `lidskii_last` is the p = 1 case combined with an entrywise bound) as a new eval problem: for self-adjoint complex matrices A, B with eigenvalues sorted in the same order and p ≥ 1, ∑_j |α_j - β_j|^p ≤ ∑_j |γ_j|^p where γ_j are the eigenvalues of B - A. Mathlib has no Lidskii, Ky Fan, or Hoffman-Wielandt perturbation bounds. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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This PR adds Lidskii's inequality as a new lean-eval challenge problem — §99 of Oliver Knill's Some Fundamental Theorems in Mathematics (an additional statement of the section; the boxed main theorem
lidskii_lastsubmitted as #274 is thep = 1case combined with an entrywise bound).For two self-adjoint complex
n × nmatricesA, Bwith eigenvalues sorted in the same order, andp ≥ 1:∑ⱼ |αⱼ − βⱼ|^p ≤ ∑ⱼ |γⱼ|^pwhere
γⱼare the eigenvalues ofB − A.mathlib has
Matrix.IsHermitian.eigenvalues₀but no classical eigenvalue-perturbation bounds (Lidskii, Ky Fan, Hoffman–Wielandt). A search found no formalization of Lidskii's inequality in any other proof assistant.Companion problem: #274
lidskii_lastis thep = 1entrywise-distance corollary.🤖 Prepared with Claude Code