Theorems · Theorem · linear algebra
Algebra.toMatrix_lsmul
∀ {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 : R),
(LinearMap.toMatrix b b) ((Algebra.lsmul R R S) x) = Matrix.diagonal fun x_1 => x- Defined in
- Mathlib.LinearAlgebra.Matrix.ToLin
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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 by1
Results whose statement or proof uses this declaration.
- Algebra.norm_algebraMap_of_basisproof · cited by 3