Theorems · Theorem · group theory

LinearEquiv.le_one_add_finrank_fixedSubmodule_dilatransvection_mul

∀ {K : Type u_1} [inst : DivisionRing K] {V : Type u_2} [inst_1 : AddCommGroup V] [inst_2 : Module K V]
  [Module.Finite K V] (e f : V ≃ₗ[K] V),
  f ∈ LinearEquiv.dilatransvections K V →
    Module.finrank K ↥(↑e).fixedSubmodule ≤ 1 + Module.finrank K ↥(↑(f * e)).fixedSubmodule

Defined in: Mathlib.LinearAlgebra.Transvection.Generation
Cited by: 1 results in Mathlib
Foundations: Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: DivisionRing AddCommGroup Module Module.Finite

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Setstatement · cited by 53,352
Modulestatement and proof · cited by 20,661
RingHom.idstatement and proof · cited by 18,349
AddCommGroupstatement and proof · cited by 12,871
Submodulestatement · cited by 7,192
LinearEquivstatement and proof · cited by 3,317
Nat.cast_oneproof · cited by 2,501
Module.finrankstatement and proof · cited by 1,770
LinearEquiv.toLinearMapstatement and proof · cited by 1,171
DivisionRingstatement and proof · cited by 1,062
Module.Finitestatement and proof · cited by 1,032
Nat.cast_addproof · cited by 586

Cited by1

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LinearEquiv.finrank_fixedSubmodule_dilatransvection_mul_leproof · cited by 1