Mathlib Map

Theorems · Theorem · linear algebra

mulLeftLinearMap_eq_mulLeft

∀ {m : Type u_2} (R : Type u_5) {A : Type u_6} [inst : Fintype m] [inst_1 : Semiring R]
  [inst_2 : NonUnitalNonAssocSemiring A] [inst_3 : Module R A] [inst_4 : SMulCommClass R A A],
  mulLeftLinearMap m R = LinearMap.mulLeft R

On square matrices, Matrix.mulLeftLinearMap and LinearMap.mulLeft coincide.

Defined in
Mathlib.LinearAlgebra.Matrix.Bilinear
Cited by
0 results in Mathlib
Foundations
Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FintypeSemiringNonUnitalNonAssocSemiringModuleSMulCommClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Module · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringLinearMap · cited by 10215LinearMapFintype · cited by 7736FintypeMatrix · cited by 4303MatrixSMulCommClass · cited by 1927SMulCommClassNonUnitalNonAssocSemiring · cited by 1081NonUnitalNonAssocSemiringLinearMap.mulLeft · cited by 34LinearMap.mulLeftmulLeftLinearMap · cited by 9mulLeftLinearMapmulLeftLinearMap_eq_mulLeftCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.