Theorems · Theorem · functional analysis

LinearMap.normDet_comp

∀ {𝕜 : Type u_1} {U : Type u_2} {V : Type u_3} {W : Type u_4} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup U]
  [inst_2 : InnerProductSpace 𝕜 U] [inst_3 : FiniteDimensional 𝕜 U] [inst_4 : NormedAddCommGroup V]
  [inst_5 : InnerProductSpace 𝕜 V] [inst_6 : NormedAddCommGroup W] [inst_7 : InnerProductSpace 𝕜 W] (f : U →ₗ[𝕜] V)
  (g : V →ₗ[𝕜] W), (g ∘ₗ f).normDet = (g.domRestrict f.range).normDet * f.normDet

Defined in

Mathlib.Analysis.InnerProductSpace.NormDet

Cited by

2 results in Mathlib

Foundations

Depth 247 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceFiniteDimensionalNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpace