Theorems · Theorem · linear algebra

FiniteDimensional.of_surjective

∀ {K : Type u} {V : Type v} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] {V₂ : Type v'}
  [inst_3 : AddCommGroup V₂] [inst_4 : Module K V₂] (f : V →ₗ[K] V₂),
  Function.Surjective ⇑f → ∀ [FiniteDimensional K V], FiniteDimensional K V₂

If the domain of a surjective linear map is finite dimensional, the codomain must be as well.

Defined in

Mathlib.LinearAlgebra.FiniteDimensional.Defs

Cited by

1 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleAddCommGroupModuleFiniteDimensional