Theorems · Theorem · linear algebra
Matrix.det_updateRow_add_smul_self
∀ {n : Type u_2} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] (A : Matrix n n R)
{i j : n}, i ≠ j → ∀ (c : R), (A.updateRow i (A i + c • A j)).det = A.det- Cited by
- 4 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintypeCommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Matrixstatement and proof · cited by 4,303
- add_zeroproof · cited by 2,707
- MulZeroClass.mul_zeroproof · cited by 2,091
- Matrix.detstatement and proof · cited by 665
- Matrix.det.congr_simpproof · cited by 91
- Matrix.updateRowstatement and proof · cited by 63
- Matrix.updateRow_selfproof · cited by 19
- Matrix.updateRow_neproof · cited by 16
- Matrix.updateRow_eq_selfproof · cited by 7
- Matrix.det_zero_of_row_eqproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- Matrix.det_transvection_of_neproof · cited by 1
- Matrix.det_eq_of_forall_row_eq_smul_add_const_auxproof · cited by 1
- Matrix.det_eq_of_forall_row_eq_smul_add_pred_auxproof · cited by 1
- Matrix.det_updateCol_add_smul_selfproof · cited by 0