Theorems · Theorem · linear algebra
Module.End.hasEigenvalue_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}, f.HasEigenvalue μ ↔ f.eigenspace μ ≠ ⊥- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 68 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.
Cites8
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
- Submodulestatement · cited by 7,192
- Bot.botstatement · cited by 4,720
- Module.Endstatement and proof · cited by 774
- Module.End.HasEigenvaluestatement · cited by 56
- Module.End.eigenspacestatement · cited by 56
Cited by5
Results whose statement or proof uses this declaration.
- det_ne_zero_of_sum_row_lt_diagproof · cited by 1
- Module.End.hasEigenvalue_iff_isRoot_charpolyproof · cited by 1
- Module.End.HasEigenvalue.nonemptyproof · cited by 0
- Module.End.IsSemisimple.eq_zero_iff_forall_eigenvalueproof · cited by 0
- RootPairing.Base.det_four_sub_cartanMatrix_ne_zeroproof · cited by 0