Theorems · Theorem · linear algebra
LinearMap.support_singularValues
∀ {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), T.singularValues.support = Finset.range (Module.finrank 𝕜 ↥T.range)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 262 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement · cited by 25,697
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- Finsetstatement and proof · cited by 13,712
- LinearMapstatement and proof · cited by 10,215
- SetLike.coeproof · cited by 8,199
- Submodulestatement · cited by 7,192
- Set.univproof · cited by 3,945
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- Finset.cardproof · cited by 2,327
Cited by3
Results whose statement or proof uses this declaration.
- LinearMap.singularValues_eq_zero_iff_le_finrank_rangeproof · cited by 2
- LinearMap.singularValues_pos_iff_lt_finrank_rangeproof · cited by 0
- LinearMap.singularValues_finrank_range_selfproof · cited by 0