Theorems · Theorem · functional analysis

LinearIsometry.normDet_eq_one

∀ {𝕜 : Type u_1} {U : Type u_2} {V : Type u_3} [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] (f : U →ₗᵢ[𝕜] V), f.normDet = 1

LinearMap.normDet of a linear isometry is 1.

Defined in

Mathlib.Analysis.InnerProductSpace.NormDet

Cited by

4 results in Mathlib

Foundations

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

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceFiniteDimensionalNormedAddCommGroupInnerProductSpace