Theorems · Theorem · linear algebra
LinearMap.singularValues_of_finrank_le
∀ {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) {i : ℕ}, Module.finrank 𝕜 E ≤ i → T.singularValues i = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · 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
- Set.rangeproof · cited by 4,705
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement and proof · cited by 1,770
- Real.sqrtproof · cited by 545
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.singularValues_antitoneproof · cited by 1