Theorems · Theorem · linear algebra

LinearEquiv.isOfFinOrder_of_finite_of_span_eq_top_of_mapsTo

∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {Φ : Set M},
  Φ.Finite → Submodule.span R Φ = ⊤ → ∀ {e : M ≃ₗ[R] M}, Set.MapsTo (⇑e) Φ Φ → IsOfFinOrder e

A linear equivalence which preserves a finite spanning set must have finite order.

Defined in

Mathlib.LinearAlgebra.FiniteSpan

Cited by

1 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModule