Theorems · Theorem · linear algebra
Matrix.det_updateRow_smul
∀ {n : Type u_2} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] (M : Matrix n n R)
(j : n) (s : R) (u : n → R), (M.updateRow j (s • u)).det = s * (M.updateRow j u).det- Cited by
- 5 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.
Cites7
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 · cited by 665
- Matrix.updateRowstatement · cited by 63
- Matrix.detRowAlternatingproof · cited by 14
- AlternatingMap.map_update_smulproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Matrix.det_updateRow_add_smul_selfproof · cited by 4
- Matrix.det_updateCol_smulproof · cited by 2
- Matrix.det_updateRow_sum_auxproof · cited by 1
- Matrix.det_vecMulVecproof · cited by 0
- Polynomial.resultant_derivproof · cited by 0