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Theorems · Theorem · functional analysis

LinearMap.normDet.congr_simp

∀ {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 f_1 : U →ₗ[𝕜] V), f = f_1 → f.normDet = f_1.normDet
Defined in
Mathlib.Analysis.InnerProductSpace.NormDet
Cited by
2 results in Mathlib
Foundations
Depth 242 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RCLikeNormedAddCommGroupInnerProductSpaceFiniteDimensionalNormedAddCommGroupInnerProductSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

LinearMap.normDet_smul · cited by 1LinearMap.normDet_smulLinearMap.normDet_neg · cited by 0LinearMap.normDet_negReal · cited by 25697RealRingHom.id · cited by 18349RingHom.idNormedAddCommGroup · cited by 15752NormedAddCommGroupLinearMap · cited by 10215LinearMapInnerProductSpace · cited by 3523InnerProductSpaceRCLike · cited by 2829RCLikeFiniteDimensional · cited by 1854FiniteDimensionalLinearMap.normDet · cited by 27LinearMap.normDetnormDet.congr_simpCITED BYCITES

Cites8

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Cited by2

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