Theorems · Theorem · nonassociative algebras
skewAdjointMatricesLieSubalgebraEquiv_apply
∀ {R : Type u} {n : Type w} [inst : CommRing R] [inst_1 : Fintype n] (J : Matrix n n R) [inst_2 : DecidableEq n]
(P : Matrix n n R) (h : Invertible P) (A : ↥(skewAdjointMatricesLieSubalgebra J)),
↑((skewAdjointMatricesLieSubalgebraEquiv J P h) A) = P⁻¹ * ↑A * P- Defined in
- Mathlib.Algebra.Lie.SkewAdjoint
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingFintypeDecidableEq
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.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Invertiblestatement and proof · cited by 549
- LieSubalgebrastatement · cited by 418
- Matrix.transposestatement · cited by 389
- LieRing.ofAssociativeRingstatement · cited by 227
- LieEquivstatement · cited by 86
- skewAdjointMatricesLieSubalgebrastatement and proof · cited by 5
- skewAdjointMatricesLieSubalgebraEquivstatement · cited by 2
- Matrix.lieConj_symm_applyproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- LieAlgebra.Orthogonal.soIndefiniteEquiv_applyproof · cited by 0