Theorems · Theorem · group theory
Matrix.GeneralLinearGroup.mem_center_iff_val_eq_scalar
Deprecated since 2026-02-08Use Matrix.GeneralLinearGroup.mem_center_iff_val_mem_range_scalar instead.
∀ {R : Type u_1} {n : Type u_2} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommRing R] {g : GL n R},
g ∈ Subgroup.center (GL n R) ↔ ↑g ∈ Set.range ⇑(Matrix.scalar n)Alias of Matrix.GeneralLinearGroup.mem_center_iff_val_mem_range_scalar.
The center of GL n R consists of scalar matrices.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEqCommRing
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- CommRingstatement · cited by 17,173
- RingHomstatement · cited by 10,189
- Fintypestatement · cited by 7,736
- Set.rangestatement · cited by 4,705
- Matrixstatement · cited by 4,303
- Subgroupstatement · cited by 3,593
- Units.valstatement · cited by 1,966
- Matrix.GeneralLinearGroupstatement · cited by 556
- Subgroup.centerstatement · cited by 121
- Matrix.scalarstatement · cited by 62
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