Theorems · Theorem · linear algebra

LinearMap.transvection.comp_of_right_eq_apply

∀ {R : Type u_1} {V : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid V] [inst_2 : Module R V]
  {f g : Module.Dual R V} {v x : V},
  f v = 0 → (LinearMap.transvection f v) ((LinearMap.transvection g v) x) = (LinearMap.transvection (f + g) v) x

Defined in: Mathlib.LinearAlgebra.Transvection.Basic
Cited by: 3 results in Mathlib
Foundations: Depth 25 from the axioms · uses propext, Quot.sound
Assumes: Semiring AddCommMonoid Module

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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
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
map_addproof · cited by 964
add_assocproof · cited by 746
zero_smulproof · cited by 716
Module.Dualstatement and proof · cited by 583
map_smulproof · cited by 566

Cited by3

Results whose statement or proof uses this declaration.

LinearEquiv.transvection.symm_eq'proof · cited by 1
LinearMap.transvection.comp_of_right_eqproof · cited by 0
LinearEquiv.transvection.trans_of_right_eqproof · cited by 0