Theorems · Theorem · linear algebra
Matrix.scalar_comm_iff
∀ {m : Type u_2} {n : Type u_3} {α : Type u_11} [inst : Semiring α] [inst_1 : DecidableEq n] [inst_2 : Fintype n]
[inst_3 : DecidableEq m] [inst_4 : Fintype m] {r : α} {M : Matrix m n α},
(Matrix.scalar m) r * M = M * (Matrix.scalar n) r ↔ r • M = MulOpposite.op r • MA version of Matrix.scalar_commute_iff for rectangular matrices.
- Defined in
- Mathlib.Data.Matrix.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- MulOppositestatement · cited by 1,135
- MulOpposite.opstatement and proof · cited by 520
- Matrix.diagonalproof · cited by 314
- Matrix.scalarstatement · cited by 62
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.scalar_commproof · cited by 4
- Matrix.scalar_commute_iffproof · cited by 2