Theorems · Theorem · linear algebra
Algebra.leftMulMatrix_apply
∀ {R : Type u_1} {S : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring S] [inst_2 : Algebra R S] {m : Type u_3}
[inst_3 : Fintype m] [inst_4 : DecidableEq m] (b : Module.Basis m R S) (x : S),
(Algebra.leftMulMatrix b) x = (LinearMap.toMatrix b b) ((Algebra.lmul R S) x)- Defined in
- Mathlib.LinearAlgebra.Matrix.ToLin
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- LinearEquivstatement · cited by 3,317
- AlgHomstatement · cited by 3,236
- Module.Basisstatement and proof · cited by 1,477
- Module.Endstatement · cited by 774
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.leftMulMatrix_eq_repr_mulproof · cited by 4
- PowerBasis.leftMulMatrixproof · cited by 0