Theorems · Theorem · linear algebra

LinearMap.singularValues_antitone

∀ {𝕜 : Type u_1} [inst : RCLike 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  [inst_3 : FiniteDimensional 𝕜 E] {F : Type u_3} [inst_4 : NormedAddCommGroup F] [inst_5 : InnerProductSpace 𝕜 F]
  [inst_6 : FiniteDimensional 𝕜 F] (T : E →ₗ[𝕜] F), Antitone ⇑T.singularValues

Defined in: Mathlib.Analysis.InnerProductSpace.SingularValues
Cited by: 1 results in Mathlib
Foundations: Depth 260 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: RCLike NormedAddCommGroup InnerProductSpace FiniteDimensional NormedAddCommGroup InnerProductSpace FiniteDimensional

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Cites20

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Realstatement and proof · cited by 25,697
RingHom.idstatement and proof · cited by 18,349
NormedAddCommGroupstatement and proof · cited by 15,752
LinearMapstatement and proof · cited by 10,215
Finsuppstatement · cited by 5,255
InnerProductSpacestatement and proof · cited by 3,523
RCLikestatement and proof · cited by 2,829
FiniteDimensionalstatement and proof · cited by 1,854
Module.finrankproof · cited by 1,770
LE.le.trans_ltproof · cited by 795
Antitonestatement · cited by 563

Cited by1

Results whose statement or proof uses this declaration.

LinearMap.isLowerSet_support_singularValuesproof · cited by 1