Theorems · Theorem · linear algebra
Matrix.charpoly_toLin
∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
[inst_3 : Module.Free R M] [inst_4 : Module.Finite R M] {n : Type u_5} [inst_5 : Fintype n] [inst_6 : DecidableEq n]
(A : Matrix n n R) (b : Module.Basis n R M), ((Matrix.toLin b b) A).charpoly = A.charpoly- Defined in
- Mathlib.LinearAlgebra.Charpoly.ToMatrix
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Polynomialstatement · cited by 5,681
- Matrixstatement and proof · cited by 4,303
- LinearEquivstatement · cited by 3,317
- Module.Basisstatement and proof · cited by 1,477
- Module.Finitestatement and proof · cited by 1,032
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.charpoly_toLin'proof · cited by 1