Theorems · Theorem · linear algebra

LinearEquiv.finiteDimensional

∀ {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) [FiniteDimensional K V], FiniteDimensional K V₂

Finite dimensionality is preserved under linear equivalence.

Defined in

Mathlib.LinearAlgebra.FiniteDimensional.Defs

Cited by

11 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleAddCommGroupModuleFiniteDimensional