Theorems · Theorem · linear algebra
LinearMap.transvection.of_left_eq_zero
∀ {R : Type u_1} {V : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid V] [inst_2 : Module R V] (v : V),
LinearMap.transvection 0 v = LinearMap.id- Defined in
- Mathlib.LinearAlgebra.Transvection.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement · cited by 10,215
- add_zeroproof · cited by 2,707
- LinearMap.extproof · cited by 844
- zero_smulproof · cited by 716
- LinearMap.idstatement · cited by 625
- Module.Dualstatement · cited by 583
- LinearMap.transvectionstatement · cited by 32
Cited by2
Results whose statement or proof uses this declaration.
- LinearEquiv.transvection.of_left_eq_zeroproof · cited by 2
- LinearEquiv.transvection.symm_eq'proof · cited by 1