Theorems · Theorem · linear algebra
Matrix.charmatrix_apply_ne
∀ {R : Type u_1} [inst : CommRing R] {n : Type u_4} [inst_1 : DecidableEq n] [inst_2 : Fintype n] (M : Matrix n n R)
(i j : n), i ≠ j → M.charmatrix i j = -Polynomial.C (M i j)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 102 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.
Cites12
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
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Fintypestatement and proof · cited by 7,736
- Polynomialstatement and proof · cited by 5,681
- Matrixstatement and proof · cited by 4,303
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Matrix.diagonalproof · cited by 314
- RingHom.mapMatrix_applyproof · cited by 73
- Matrix.diagonal_apply_neproof · cited by 50
- Matrix.charmatrixstatement · cited by 42
Cited by6
Results whose statement or proof uses this declaration.
- Matrix.matPolyEquiv_charmatrixproof · cited by 3
- Matrix.charpoly_sub_scalarproof · cited by 1
- matPolyEquiv_eq_X_pow_sub_Cproof · cited by 1
- Matrix.charmatrix_reindexproof · cited by 1
- Matrix.charmatrix_apply_natDegree_leproof · cited by 1
- Matrix.charmatrix_apply_natDegreeproof · cited by 0