Left inverse via the adjugate
ProvedExactVacuumAtlas.eq_inv_smul_adjugateeinstein-maxwellexact-spacetime-atlas-ivexact-vacuum-atlasgeneral-relativity
Left inverse via the adjugate
If J · K = 1 then K = (det J)⁻¹ • adjugate J.
Scope. Exactly the hypotheses printed in the formal statement.
中文摘要 由伴随矩阵表示逆。
Preamble
import Mathlib
import Definitions.Def_Atlas_Core_Basic
import Definitions.Def_Atlas_Transport_MatrixCalc
open scoped ContDiff
open ExactVacuumAtlas
variable {n : ℕ}
Formal statement
theorem ExactVacuumAtlas.eq_inv_smul_adjugate {J K : Matrix (Fin n) (Fin n) ℝ} (h : J * K = 1) :
K = (J.det)⁻¹ • J.adjugate := by sorrySource
He Wang, Exact Spacetime Atlas IV: Certified Einstein–Maxwell Backgrounds and First Variations. Local source, no public repository; commit 543904bfcfa3bb169f43fc4d9dbd569999b71886; Atlas/Transport/MatrixCalc.lean#L231-L242; SHA-256 994bf6c8664b9c7b2def61b44cb0205ed97883699045a73e41d873029c259310. Registered definitions and literature: mission/PHYSICS_BOUNDARY.md (§H–§J); Müller–Grave arXiv:0904.4184; Newman et al., J. Math. Phys. 6 (1965) 918.
Human review
Confirmed by the mission captain (proposal self-audit).
Confirmed by the moderator at approval.