Theorems · Theorem · linear algebra
Matrix.adjugate_mul_distrib_aux
∀ {n : Type v} {α : Type w} [inst : DecidableEq n] [inst_1 : Fintype n] [inst_2 : CommRing α] (A B : Matrix n n α),
IsLeftRegular A.det → IsLeftRegular B.det → (A * B).adjugate = B.adjugate * A.adjugate- Defined in
- Mathlib.LinearAlgebra.Matrix.Adjugate
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 100 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.
Cites17
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
- mul_commproof · cited by 2,262
- Matrix.detstatement and proof · cited by 665
- smul_smulproof · cited by 360
- IsLeftRegularstatement and proof · cited by 97
- Matrix.adjugatestatement and proof · cited by 64
- Matrix.mul_assocproof · cited by 56
- Matrix.det_mulproof · cited by 51
- IsRegular.leftproof · cited by 39
- Matrix.one_mulproof · cited by 30
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.adjugate_mul_distribproof · cited by 3