Theorems · Theorem · linear algebra
Matrix.det_eq_sum_mul_adjugate_row
∀ {n : Type v} {α : Type w} [inst : DecidableEq n] [inst_1 : Fintype n] [inst_2 : CommRing α] (A : Matrix n n α)
(i : n), A.det = ∑ j, A i j * A.adjugate j i- Defined in
- Mathlib.LinearAlgebra.Matrix.Adjugate
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 99 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.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- AddCommMonoidproof · cited by 12,281
- Equivproof · cited by 8,337
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement and proof · cited by 5,195
- Matrixstatement and proof · cited by 4,303
- Equiv.symmproof · cited by 3,681
- Finset.univstatement and proof · cited by 3,473
- Finset.sum_congrproof · cited by 2,323
- mul_assocproof · cited by 1,667
- Fintype.cardproof · cited by 1,386
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.det_eq_sum_mul_adjugate_colproof · cited by 0