Theorems · Theorem · linear algebra
Matrix.det.congr_simp
∀ {n : Type u_2} {inst : DecidableEq n} [inst_1 : DecidableEq n] [inst_2 : Fintype n] {R : Type v} [inst_3 : CommRing R]
(M M_1 : Matrix n n R), M = M_1 → M.det = M_1.det- Cited by
- 91 results in Mathlib
- Foundations
- Depth 87 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.
Cites4
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
- Matrix.detstatement and proof · cited by 665
Cited by91
Results whose statement or proof uses this declaration.
- RingHom.map_detproof · cited by 41
- Polynomial.resultant_zero_left_degproof · cited by 13
- Polynomial.resultant_map_mapproof · cited by 10
- Matrix.det_succ_rowproof · cited by 6
- Matrix.det_eq_sign_charpoly_coeffproof · cited by 5
- LinearMap.det_smulproof · cited by 5
- LinearMap.normDet_eq_zero_iff_ker_ne_botproof · cited by 5
- Matrix.det_succ_row_zeroproof · cited by 5
- Matrix.det_vandermondeproof · cited by 5
- Polynomial.resultant_C_mul_rightproof · cited by 5
- Module.Basis.det_selfproof · cited by 4
- Matrix.det_updateRow_add_smul_selfproof · cited by 4