Theorems · Theorem · linear algebra
Matrix.transpose_permMatrix
∀ {n : Type u_1} {R : Type u_2} [inst : DecidableEq n] (σ : Equiv.Perm n) [inst_1 : Zero R] [inst_2 : One R],
(Equiv.Perm.permMatrix R σ).transpose = Equiv.Perm.permMatrix R σ⁻¹- Defined in
- Mathlib.LinearAlgebra.Matrix.Permutation
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqZeroOne
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Matrixstatement and proof · cited by 4,303
- Equiv.Permstatement and proof · cited by 1,375
- Matrix.transposestatement · cited by 389
- PEquivproof · cited by 75
- PEquiv.toMatrixproof · cited by 25
- Equiv.Perm.permMatrixstatement and proof · cited by 25
- Equiv.toPEquivproof · cited by 23
- Equiv.Perm.inv_defproof · cited by 3
- Equiv.toPEquiv_symmproof · cited by 2
- PEquiv.toMatrix_symmproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.transpose_swapproof · cited by 1
- Matrix.conjTranspose_permMatrixproof · cited by 1