Theorems · Theorem · linear algebra
Module.End.eigenspace_mem_invtSubmodule
∀ {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.eigenspace μ ∈ f.invtSubmodule- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 73 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.
Cites9
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
- Module.Endstatement and proof · cited by 774
- Sublatticestatement · cited by 225
- Module.End.invtSubmodulestatement · cited by 93
- Module.End.eigenspacestatement · cited by 56
- Module.End.genEigenspace_mem_invtSubmoduleproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Module.End.restrict_eigenspacestatement · cited by 1
- ContinuousLinearMap.finite_dimensional_eigenspaceproof · cited by 0