Theorems · Theorem · linear algebra
Module.End.HasEigenvalue.exists_hasEigenvector
∀ {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 → ∃ v, f.HasEigenvector μ v- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Basic
- Cited by
- 8 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.
Cites7
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.HasEigenvaluestatement and proof · cited by 56
- Module.End.HasEigenvectorstatement · cited by 23
- Submodule.exists_mem_ne_zero_of_ne_botproof · cited by 9
Cited by8
Results whose statement or proof uses this declaration.
- eigenvalue_mem_ballproof · cited by 1
- LinearMap.IsSymmetric.conj_eigenvalue_eq_selfproof · cited by 1
- Matrix.lt_two_mul_of_mul_diagonal_posDef_of_for_le_of_hasEigenproof · cited by 1
- exists_root_adjoin_eq_top_of_isCyclicproof · cited by 1
- eigenvalue_nonneg_of_nonnegproof · cited by 0
- eigenvalue_pos_of_posproof · cited by 0
- LieModule.exists_nontrivial_weightSpace_of_lieIdealproof · cited by 0
- IsSl2Triple.exists_hasPrimitiveVectorWithproof · cited by 0