Theorems · Theorem · linear algebra
LinearEquiv.transvection.of_left_eq_zero
∀ {R : Type u_1} {V : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup V] [inst_2 : Module R V] (v : V)
(hv : optParam (0 v = 0) ⋯), LinearEquiv.transvection hv = LinearEquiv.refl R V- Defined in
- Mathlib.LinearAlgebra.Transvection.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
- Assumes
- RingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Ringstatement and proof · cited by 7,463
- LinearEquivstatement · cited by 3,317
- LinearEquiv.reflstatement · cited by 143
- LinearEquiv.extproof · cited by 72
- LinearMap.zero_applystatement · cited by 35
- LinearMap.transvectionproof · cited by 32
- AddHom.mk.congr_simpproof · cited by 29
Cited by2
Results whose statement or proof uses this declaration.
- LinearEquiv.refl_mem_transvectionsproof · cited by 1