Theorems · Theorem · linear algebra
Matrix.mem_range_scalar_iff_commute_transvectionStruct
∀ {n : Type u_1} {R : Type u₂} [inst : DecidableEq n] [inst_1 : CommRing R] [inst_2 : Fintype n] {M : Matrix n n R},
M ∈ Set.range ⇑(Matrix.scalar n) ↔ ∀ (t : Matrix.TransvectionStruct n R), Commute t.toMatrix M- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqCommRingFintype
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Cites24
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
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Fintypestatement and proof · cited by 7,736
- Set.rangestatement and proof · cited by 4,705
- Matrixstatement and proof · cited by 4,303
- mul_oneproof · cited by 3,885
- Commutestatement and proof · cited by 639
- smul_eq_mulproof · cited by 357
- Matrix.singleproof · cited by 129
- Matrix.scalarstatement and proof · cited by 62
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