Theorems · Definition · linear algebra
Module.End.HasGenEigenvalue
{R : Type v} →
{M : Type w} → [inst : CommRing R] → [inst_1 : AddCommGroup M] → [inst_2 : Module R M] → Module.End R M → R → ℕ → PropA scalar μ is a generalized eigenvalue for a linear map f and an exponent k ∈ ℕ if there
are generalized eigenvectors for f, k, and μ.
- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Module.Endstatement and proof · cited by 774
- Module.End.HasUnifEigenvalueproof · cited by 18
Cited by6
Results whose statement or proof uses this declaration.
- Module.End.hasEigenvalue_of_hasGenEigenvaluestatement and proof · cited by 1
- Module.End.hasGenEigenvalue_iffstatement · cited by 0
- Module.End.hasGenEigenvalue_iff_hasEigenvaluestatement · cited by 0
- Module.End.hasGenEigenvalue_of_hasEigenvaluestatement · cited by 0
- Module.End.hasGenEigenvalue_of_hasGenEigenvalue_of_lestatement and proof · cited by 0
- Module.End.exp_ne_zero_of_hasGenEigenvaluestatement and proof · cited by 0