Theorems · Theorem · linear algebra
Matrix.mem_range_scalar_of_commute_single
∀ {n : Type u_3} {α : Type u_7} [inst : DecidableEq n] [inst_1 : Fintype n] [inst_2 : Semiring α] {M : Matrix n n α},
(Pairwise fun i j => Commute (Matrix.single i j 1) M) → M ∈ Set.range ⇑(Matrix.scalar n)M is a scalar matrix if it commutes with every non-diagonal single.
- Defined in
- Mathlib.Data.Matrix.Basis
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintypeSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Setstatement · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Fintypestatement and proof · cited by 7,736
- Set.rangestatement · cited by 4,705
- Matrixstatement and proof · cited by 4,303
- IsEmptyproof · cited by 759
- Commutestatement and proof · cited by 639
- Matrix.extproof · cited by 540
- Pairwisestatement and proof · cited by 516
- isEmpty_or_nonemptyproof · cited by 269
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.mem_range_scalar_of_commute_transvectionStructproof · cited by 3
- Matrix.mem_range_scalar_iff_commute_singleproof · cited by 2