Theorems · Theorem · linear algebra
Matrix.center_eq_range
∀ {n : Type u_3} (R : Type u_5) [inst : DecidableEq n] [inst_1 : Fintype n] [inst_2 : CommSemiring R],
Set.center (Matrix n n R) = Set.range ⇑(Matrix.scalar n)For a commutative semiring R, the center of Matrix n n R is the range of scalar n
(i.e., the span of {1}).
- Defined in
- Mathlib.Data.Matrix.Basis
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
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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 and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Fintypestatement and proof · cited by 7,736
- Set.imageproof · cited by 5,609
- Set.rangestatement and proof · cited by 4,705
- Matrixstatement and proof · cited by 4,303
- Set.image_univproof · cited by 322
- Matrix.scalarstatement and proof · cited by 62
- Set.centerstatement · cited by 49
- Set.center_eq_univproof · cited by 10
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