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Theorems · Definition · group theory

Matrix.SpecialLinearGroup.diag2n

{F : Type u_1} →
  [inst : Field F] →
    {ι : Type u_2} →
      [inst_1 : Fintype ι] →
        [inst_2 : DecidableEq ι] → {i j : ι} → i ≠ j → (a : F) → a ≠ 0 → Matrix.SpecialLinearGroup ι F

An element in SLₙ(F) induced by a diagonal matrix 1 on any other entries and a, a⁻¹ on positition i and j respectively where i ≠ j.

Defined in
Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup
Cited by
7 results in Mathlib
Foundations
Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldFintypeDecidableEq
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matrix.SpecialLinearGroup.diag2 · cited by 13SpecialLinearGroup.diag2Matrix.SpecialLinearGroup.diag_commute · cited by 2SpecialLinearGroup.diag_c…Matrix.SL2.transvection_induction · cited by 2SL2.transvection_inductionMatrix.SpecialLinearGroup.diag_eq_diag2n_prod · cited by 1SpecialLinearGroup.diag_e…Matrix.SpecialLinearGroup.diagonal_transvection_induction' · cited by 1SpecialLinearGroup.diagon…Matrix.SpecialLinearGroup.diag2n_coe · cited by 0SpecialLinearGroup.diag2n…Matrix.SpecialLinearGroup.diag2n.congr_simp · cited by 0diag2n.congr_simpMatrix.SpecialLinearGroup.diag2_def · cited by 0SpecialLinearGroup.diag2_…Fintype · cited by 7736FintypeField · cited by 7404FieldMatrix.SpecialLinearGroup · cited by 348Matrix.SpecialLinearGroupMatrix.diagonal · cited by 314Matrix.diagonalSpecialLinearGroup.diag2nCITED BYCITES

Cites4

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Cited by8

Results whose statement or proof uses this declaration.