Theorems · Theorem · nonassociative algebras
LieModule.toEnd_matrix
∀ {R : Type u} [inst : CommRing R] {n : Type w} [inst_1 : DecidableEq n] [inst_2 : Fintype n],
LieModule.toEnd R (Matrix n n R) (n → R) = lieEquivMatrix'.symm.toLieHom- Defined in
- Mathlib.Algebra.Lie.Matrix
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingDecidableEqFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- one_smulproof · cited by 1,374
- MulOppositeproof · cited by 1,135
- Module.Endstatement · cited by 774
- Pi.singleproof · cited by 518
- LieHomstatement · cited by 382
- LieRing.ofAssociativeRingstatement · cited by 227
- LinearMap.ext_ringproof · cited by 152
- LieModule.toEndstatement · cited by 144
- LieModule.toEnd_apply_applyproof · cited by 39
Cited by2
Results whose statement or proof uses this declaration.
- RootPairing.GeckConstruction.coe_genWeightSpace_zero_eq_span_range_uproof · cited by 0
- RootPairing.GeckConstruction.trace_toEnd_eq_zeroproof · cited by 0