Theorems · Theorem · linear algebra
LinearMap.hasEigenvalue_adjoint_comp_self_sq_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) {n : ℕ},
n < Module.finrank 𝕜 E → Module.End.HasEigenvalue (LinearMap.adjoint T ∘ₗ T) (↑(T.singularValues n) ^ 2)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 260 from the axioms · uses propext, Classical.choice, Quot.sound
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- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Moduleproof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingproof · cited by 17,173
- NormedAddCommGroupstatement and proof · cited by 15,752
- AddCommGroupproof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Finsuppstatement · cited by 5,255
- Algebra.algebraMapproof · cited by 4,706
- InnerProductSpacestatement and proof · cited by 3,523
- LinearEquivstatement · cited by 3,317
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