Theorems · Theorem · linear algebra
Module.End.mem_spectrum_iff_isRoot_charpoly
∀ {K : Type u_3} {V : Type u_4} [inst : Field K] [inst_1 : AddCommGroup V] [inst_2 : Module K V]
[inst_3 : Module.Finite K V] (f : Module.End K V) (μ : K), μ ∈ spectrum K f ↔ (LinearMap.charpoly f).IsRoot μ- Cited by
- 0 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- Module.Finitestatement and proof · cited by 1,032
- Module.Endstatement and proof · cited by 774
- spectrumstatement · cited by 510
- Polynomial.IsRootstatement and proof · cited by 152
- LinearMap.charpolystatement and proof · cited by 67
- Module.End.hasEigenvalue_iff_mem_spectrumproof · cited by 4
- Module.End.hasEigenvalue_iff_isRoot_charpolyproof · cited by 1
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