Theorems · Theorem · linear algebra
Matrix.det_smul_inv_vecMul_eq_cramer_transpose
∀ {n : Type u'} {α : Type v} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommRing α] (A : Matrix n n α)
(b : n → α), IsUnit A.det → A.det • Matrix.vecMul b A⁻¹ = A.transpose.cramer bOne form of Cramer's rule. See Matrix.mulVec_cramer for a stronger form.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEqCommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- LinearMapstatement · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- IsUnitstatement and proof · cited by 1,602
- Matrix.detstatement and proof · cited by 665
- Matrix.transposestatement and proof · cited by 389
- Matrix.mulVecproof · cited by 267
- Matrix.vecMulstatement and proof · cited by 148
- Matrix.det_transposeproof · cited by 51
Cited by1
Results whose statement or proof uses this declaration.
- AffineBasis.det_smul_coords_eq_cramer_coordsproof · cited by 0