Theorems · Theorem · linear algebra

LinearMap.lcomp_injective_of_surjective

∀ {R : Type u_1} {S : Type u_3} [inst : Semiring R] [inst_1 : Semiring S] {M : Type u_5} {M₂ : Type u_6} {N : Type u_7}
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : AddCommMonoid N] [inst_5 : Module R M]
  [inst_6 : Module R M₂] [inst_7 : Module S N] [inst_8 : Module R N] [inst_9 : SMulCommClass R S N] (g : M →ₗ[R] M₂),
  Function.Surjective ⇑g → Function.Injective ⇑(LinearMap.lcomp S N g)

Defined in

Mathlib.LinearAlgebra.BilinearMap

Cited by

1 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModuleModuleSMulCommClass