Theorems · Theorem · linear algebra
Module.End.HasEigenvalue.nonempty
∀ {R : Type u_1} {n : Type u_2} [inst : DecidableEq n] [inst_1 : Fintype n] [inst_2 : CommRing R] {A : Matrix n n R}
{μ : R}, Module.End.HasEigenvalue (Matrix.toLin' A) μ → Nonempty n- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Matrix
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintypeCommRing
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Cites14
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- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Bot.botproof · cited by 4,720
- Matrixstatement and proof · cited by 4,303
- LinearEquivstatement · cited by 3,317
- IsEmptyproof · cited by 759
- Matrix.toLin'statement and proof · cited by 86
- Module.End.HasEigenvaluestatement and proof · cited by 56
- Module.End.eigenspaceproof · cited by 56
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