Theorems · Theorem · linear algebra
Matrix.adjugate_apply
∀ {n : Type v} {α : Type w} [inst : DecidableEq n] [inst_1 : Fintype n] [inst_2 : CommRing α] (A : Matrix n n α)
(i j : n), A.adjugate i j = (A.updateRow j (Pi.single i 1)).det- Defined in
- Mathlib.LinearAlgebra.Matrix.Adjugate
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintypeCommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Matrix.detstatement and proof · cited by 665
- Pi.singlestatement and proof · cited by 518
- Matrix.transposeproof · cited by 389
- Matrix.adjugatestatement · cited by 64
- Matrix.updateRowstatement and proof · cited by 63
- Matrix.det_transposeproof · cited by 51
- Matrix.cramerproof · cited by 27
- Matrix.of_applyproof · cited by 15
Cited by5
Results whose statement or proof uses this declaration.
- Matrix.adjugate_transposeproof · cited by 5
- Matrix.adjugate_subsingletonproof · cited by 4
- RingHom.map_adjugateproof · cited by 3
- Matrix.adjugate_fin_succ_eq_det_submatrixproof · cited by 2
- Matrix.adjugate_submatrix_equiv_selfproof · cited by 1