Theorems · Theorem · linear algebra

LinearMap.detAux_def

∀ {M : Type u_7} [inst : AddCommGroup M] {ι : Type u_8} [inst_1 : DecidableEq ι] [inst_2 : Fintype ι] {A : Type u_9}
  [inst_3 : CommRing A] [inst_4 : Module A M],
  LinearMap.detAux = Trunc.lift (fun b => Matrix.detMonoidHom.comp ↑(LinearMap.toMatrixAlgEquiv b)) ⋯

Defined in: Mathlib.LinearAlgebra.Determinant
Cited by: 1 results in Mathlib
Foundations: Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddCommGroup DecidableEq Fintype CommRing Module

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites17

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
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
LinearMapstatement · cited by 10,215
Fintypestatement and proof · cited by 7,736
Matrixstatement · cited by 4,303
MonoidHomstatement · cited by 3,629
AlgEquivstatement · cited by 1,681
Module.Basisstatement and proof · cited by 1,477
MonoidHom.compstatement and proof · cited by 469
MonoidHomClass.toMonoidHomstatement and proof · cited by 294

Cited by1

Results whose statement or proof uses this declaration.

LinearMap.detAux_def'proof · cited by 1