Theorems · Theorem · group theory

Matrix.SpecialLinearGroup.scalar_eq_self_of_mem_center

∀ {n : Type u} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R]
  {A : Matrix.SpecialLinearGroup n R},
  A ∈ Subgroup.center (Matrix.SpecialLinearGroup n R) → ∀ (i : n), (Matrix.scalar n) (↑A i i) = ↑A

Defined in: Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup
Cited by: 2 results in Mathlib
Foundations: Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: DecidableEq Fintype CommRing

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Cites17

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
CommRingstatement and proof · cited by 17,173
RingHomstatement · cited by 10,189
Fintypestatement and proof · cited by 7,736
Matrixstatement · cited by 4,303
Subgroupstatement · cited by 3,593
Matrix.detstatement · cited by 665
Matrix.SpecialLinearGroupstatement and proof · cited by 348
Matrix.diagonalproof · cited by 314
Subgroup.centerstatement and proof · cited by 121
Matrix.diagonal_apply_eqproof · cited by 64
Matrix.scalarstatement and proof · cited by 62

Cited by2

Results whose statement or proof uses this declaration.

Matrix.SpecialLinearGroup.mem_center_iffproof · cited by 2
Matrix.SpecialLinearGroup.scalar_eq_coe_self_centerproof · cited by 1