Theorems · Theorem · linear algebra
Matrix.conjTranspose_permMatrix
∀ {n : Type u_1} {R : Type u_2} [inst : DecidableEq n] (σ : Equiv.Perm n) [inst_1 : NonAssocSemiring R]
[inst_2 : StarRing R], (Equiv.Perm.permMatrix R σ).conjTranspose = Equiv.Perm.permMatrix R σ⁻¹- Defined in
- Mathlib.LinearAlgebra.Matrix.Permutation
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Matrixstatement · cited by 4,303
- Equiv.symmproof · cited by 3,681
- StarRingstatement and proof · cited by 1,686
- Equiv.Permstatement and proof · cited by 1,375
- Star.starproof · cited by 1,082
- NonAssocSemiringstatement and proof · cited by 805
- Matrix.extproof · cited by 540
- Matrix.ofproof · cited by 336
- Matrix.conjTransposestatement · cited by 202
- star_zeroproof · cited by 58
- star_oneproof · cited by 33
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.conjTranspose_swapproof · cited by 0