Theorems · Theorem · linear algebra
Module.End.iSup_genEigenspace_eq
∀ {R : Type v} {M : Type w} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (f : Module.End R M)
(μ : R), ⨆ k, (f.genEigenspace μ) ↑k = f.maxGenEigenspace μ- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
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Cites12
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
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Submodulestatement · cited by 7,192
- ENatstatement · cited by 4,985
- iSupstatement and proof · cited by 2,415
- OrderHomstatement · cited by 934
- Module.Endstatement and proof · cited by 774
- Module.End.genEigenspacestatement and proof · cited by 70
- Module.End.maxGenEigenspacestatement · cited by 41
- Module.End.genEigenspace_topproof · cited by 1
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