Theorems · Theorem · linear algebra

mulLinearMap_eq_mul

∀ {m : Type u_2} (R : Type u_5) {A : Type u_6} [inst : Fintype m] [inst_1 : CommSemiring R]
  [inst_2 : NonUnitalNonAssocSemiring A] [inst_3 : Module R A] [inst_4 : SMulCommClass R A A]
  [inst_5 : IsScalarTower R A A], mulLinearMap R = LinearMap.mul R (Matrix m m A)

On square matrices, Matrix.mulLinearMap and LinearMap.mul coincide.

Defined in: Mathlib.LinearAlgebra.Matrix.Bilinear
Cited by: 0 results in Mathlib
Foundations: Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Fintype CommSemiring NonUnitalNonAssocSemiring Module SMulCommClass IsScalarTower

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites11

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

Modulestatement and proof · cited by 20,661
RingHom.idstatement · cited by 18,349
CommSemiringstatement and proof · cited by 10,911
LinearMapstatement · cited by 10,215
Fintypestatement and proof · cited by 7,736
Matrixstatement · cited by 4,303
IsScalarTowerstatement and proof · cited by 3,896
SMulCommClassstatement and proof · cited by 1,927
NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
LinearMap.mulstatement · cited by 61
mulLinearMapstatement · cited by 2

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.