Theorems · Theorem · linear algebra
Matrix.charpoly.congr_simp
∀ {R : Type u_1} [inst : CommRing R] {n : Type u_4} {inst_1 : DecidableEq n} [inst_2 : DecidableEq n]
[inst_3 : Fintype n] (M M_1 : Matrix n n R), M = M_1 → M.charpoly = M_1.charpoly- Cited by
- 11 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingDecidableEqFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Polynomialstatement · cited by 5,681
- Matrixstatement and proof · cited by 4,303
- Matrix.charpolystatement and proof · cited by 82
Cited by11
Results whose statement or proof uses this declaration.
- LinearMap.charpoly_toMatrixproof · cited by 9
- Matrix.charpoly.univ_map_eval₂Homproof · cited by 3
- LinearMap.charpoly_sub_smulproof · cited by 2
- Matrix.charpoly_units_conjproof · cited by 2
- Matrix.IsHermitian.charpoly_eqproof · cited by 2
- Matrix.charpoly_toLinproof · cited by 1
- Matrix.charpoly_units_conj'proof · cited by 1
- LinearMap.IsSymmetric.charpoly_eqproof · cited by 1
- LinearMap.charpoly_oneproof · cited by 0
- LinearMap.charpoly_zeroproof · cited by 0
- Matrix.IsHermitian.charpoly_cfc_eqproof · cited by 0