Theorems · Theorem · linear algebra
Module.End.HasUnifEigenvalue.of_mem_spectrum
∀ {K : Type v} {V : Type w} [inst : Field K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] [FiniteDimensional K V]
{f : Module.End K V} {μ : K}, μ ∈ spectrum K f → f.HasUnifEigenvalue μ 1Alias of the reverse direction of Module.End.hasUnifEigenvalue_iff_mem_spectrum.
- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
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- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Fieldstatement and proof · cited by 7,404
- ENatstatement · cited by 4,985
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.Endstatement and proof · cited by 774
- spectrumstatement · cited by 510
- Module.End.HasUnifEigenvaluestatement · cited by 18
- Module.End.hasUnifEigenvalue_iff_mem_spectrumproof · cited by 2
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