Theorems · Theorem · linear algebra
Matrix.adjugate_conjTranspose
∀ {n : Type v} {α : Type w} [inst : DecidableEq n] [inst_1 : Fintype n] [inst_2 : CommRing α] [inst_3 : StarRing α]
(A : Matrix n n α), A.adjugate.conjTranspose = A.conjTranspose.adjugate- Defined in
- Mathlib.LinearAlgebra.Matrix.Adjugate
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- StarRingstatement and proof · cited by 1,686
- Star.starproof · cited by 1,082
- starRingEndproof · cited by 671
- Matrix.transposeproof · cited by 389
- Matrix.mapproof · cited by 247
- Matrix.conjTransposestatement · cited by 202
- Matrix.adjugatestatement and proof · cited by 64
- Matrix.adjugate_transposeproof · cited by 5
- RingHom.map_adjugateproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.conjTranspose_nonsing_invproof · cited by 5
- Matrix.IsHermitian.adjugateproof · cited by 0