Theorems · Theorem · linear algebra

Module.Dual.eq_of_ker_eq_of_apply_eq

∀ {K : Type u_1} {V₁ : Type u_2} [inst : DivisionRing K] [inst_1 : AddCommGroup V₁] [inst_2 : Module K V₁]
  [FiniteDimensional K V₁] {f g : Module.Dual K V₁} (x : V₁),
  LinearMap.ker f = LinearMap.ker g → f x = g x → f x ≠ 0 → f = g

Defined in

Mathlib.LinearAlgebra.Dual.Lemmas

Cited by

1 results in Mathlib

Foundations

Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleFiniteDimensional