Theorems · Theorem · group theory

Matrix.SpecialLinearGroup.mem_lineStab_iff

∀ {F : Type u_1} [inst : Field F] {ι : Type u_2} [inst_1 : DecidableEq ι] [inst_2 : Fintype ι]
  (A : Matrix.SpecialLinearGroup ι F) (L : Submodule F (ι → F)),
  A ∈ Matrix.SpecialLinearGroup.lineStab L ↔ ∀ (w : ι → F), A • w - w ∈ L

Defined in: Mathlib.LinearAlgebra.Projectivization.PSL.Stabilizer
Cited by: 0 results in Mathlib
Foundations: Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field DecidableEq Fintype

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Fintypestatement and proof · cited by 7,736
Fieldstatement and proof · cited by 7,404
Submodulestatement and proof · cited by 7,192
Subgroupstatement · cited by 3,593
Matrix.SpecialLinearGroupstatement and proof · cited by 348
Matrix.SpecialLinearGroup.lineStabstatement · cited by 10

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