Theorems · Theorem · linear algebra
Matrix.mul_adjugate
∀ {n : Type v} {α : Type w} [inst : DecidableEq n] [inst_1 : Fintype n] [inst_2 : CommRing α] (A : Matrix n n α),
A * A.adjugate = A.det • 1- Defined in
- Mathlib.LinearAlgebra.Matrix.Adjugate
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 97 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.
Cites23
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
- Finset.sumproof · cited by 5,195
- Matrixstatement and proof · cited by 4,303
- Finset.univproof · cited by 3,473
- Finset.sum_congrproof · cited by 2,323
- Matrix.detstatement and proof · cited by 665
- Matrix.extproof · cited by 540
- Pi.singleproof · cited by 518
- Matrix.transposeproof · cited by 389
- smul_eq_mulproof · cited by 357
Cited by10
Results whose statement or proof uses this declaration.
- Matrix.adjugate_mulproof · cited by 6
- Matrix.isRegular_of_isLeftRegular_detproof · cited by 3
- Matrix.rank_mul_eq_left_of_det_mem_nonZeroDivisorsproof · cited by 2
- Matrix.mulVec_cramerproof · cited by 2
- Polynomial.sylveserMap_comp_adjSylvesterproof · cited by 1
- Matrix.SemiconjBy.zpow_rightproof · cited by 1
- Matrix.adjugate_mul_distrib_auxproof · cited by 1
- Matrix.det_smul_adjugate_adjugateproof · cited by 1
- Matrix.det_adjugateproof · cited by 0
- Matrix.inv_adjugateproof · cited by 0