Theorems · Theorem · linear algebra

LinearMap.comap_eq_sup_ker_of_disjoint

∀ {K : Type u} {V : Type v} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] {p : Submodule K V}
  [FiniteDimensional K ↥p] {f : V →ₗ[K] V}, (∀ x ∈ p, f x ∈ p) → Disjoint p f.ker → Submodule.comap f p = p ⊔ f.ker

Defined in

Mathlib.LinearAlgebra.FiniteDimensional.Basic

Cited by

1 results in Mathlib

Foundations

Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleFiniteDimensional