Theorems · Theorem · functional analysis

ContinuousLinearMap.det_pi

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} [inst : Fintype ι] [inst_1 : CommRing R] [inst_2 : AddCommGroup M]
  [inst_3 : TopologicalSpace M] [inst_4 : Module R M] [Module.Free R M] [Module.Finite R M] (f : ι → M →L[R] M),
  (ContinuousLinearMap.pi fun i => f i ∘SL ContinuousLinearMap.proj i).det = ∏ i, (f i).det

Defined in

Mathlib.Topology.Algebra.Module.Determinant

Cited by

1 results in Mathlib

Foundations

Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeCommRingAddCommGroupTopologicalSpaceModuleModule.FreeModule.Finite