Theorems · Theorem · linear algebra
Module.End.hasGenEigenvalue_iff
∀ {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 : ℕ}, f.HasGenEigenvalue μ k ↔ (f.genEigenspace μ) ↑k ≠ ⊥- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
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Cites11
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- DFunLike.coestatement · 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
- Bot.botstatement · cited by 4,720
- OrderHomstatement · cited by 934
- Module.Endstatement and proof · cited by 774
- Module.End.genEigenspacestatement · cited by 70
- Module.End.HasGenEigenvaluestatement · cited by 6
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