Theorems · Theorem · linear algebra
Matrix.adjugate_transpose
∀ {n : Type v} {α : Type w} [inst : DecidableEq n] [inst_1 : Fintype n] [inst_2 : CommRing α] (A : Matrix n n α),
A.adjugate.transpose = A.transpose.adjugate- Defined in
- Mathlib.LinearAlgebra.Matrix.Adjugate
- Cited by
- 5 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.
Cites39
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
- Finsetproof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Finset.sumproof · cited by 5,195
- Matrixstatement and proof · cited by 4,303
- Equiv.symmproof · cited by 3,681
- Finset.univproof · cited by 3,473
- Finset.prodproof · cited by 2,356
- Finset.sum_congrproof · cited by 2,323
- CommMonoidproof · cited by 2,264
- Units.valproof · cited by 1,966
Cited by5
Results whose statement or proof uses this declaration.
- Matrix.adjugate_mulproof · cited by 6
- Matrix.transpose_nonsing_invproof · cited by 3
- Matrix.cramer_eq_adjugate_mulVecproof · cited by 2
- Matrix.adjugate_conjTransposeproof · cited by 2
- Matrix.IsSymm.adjugateproof · cited by 1