Theorems · Theorem · linear algebra
LinearMap.card_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.card = Module.finrank 𝕜 ↥T.range7.68(b) from [axler2024]. See also LinearMap.support_singularValues for a stronger statement.
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- Foundations
- Depth 259 from the axioms · uses propext, Classical.choice, Quot.sound
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- DFunLike.coeproof · 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
- Finsetproof · cited by 13,712
- LinearMapstatement and proof · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- Algebra.algebraMapproof · cited by 4,706
- InnerProductSpacestatement and proof · cited by 3,523
- Finset.univproof · cited by 3,473
- Compl.complproof · cited by 2,925
- RCLikestatement and proof · cited by 2,829
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