Theorems · Theorem · linear algebra
LinearMap.trace_one
∀ (R : Type u_1) [inst : CommRing R] (M : Type u_2) [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Module.Free R M] [Module.Finite R M], (LinearMap.trace R M) 1 = ↑(Module.finrank R M)
The trace of the identity endomorphism is the dimension of the free module.
- Defined in
- Mathlib.LinearAlgebra.Trace
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Matrixproof · cited by 4,303
- Nat.cast_oneproof · cited by 2,501
- Nontrivialproof · cited by 2,416
- Module.finrankstatement and proof · cited by 1,770
- Module.Basisproof · cited by 1,477
- Fintype.cardproof · cited by 1,386
Cited by4
Results whose statement or proof uses this declaration.
- LinearMap.trace_idproof · cited by 4
- Module.Free.bijective_algebraMap_of_finrank_eq_oneproof · cited by 1
- Representation.char_oneproof · cited by 0
- FDRep.char_oneproof · cited by 0