Theorems · Theorem · linear algebra
Matrix.detp_smul_adjp
∀ {n : Type u_1} {R : Type u_3} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommSemiring R]
{A B : Matrix n n R},
A * B = 1 →
A + (Matrix.detp 1 A • Matrix.adjp (-1) B + Matrix.detp (-1) A • Matrix.adjp 1 B) =
Matrix.detp 1 A • Matrix.adjp 1 B + Matrix.detp (-1) A • Matrix.adjp (-1) B- Cited by
- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Unitsstatement · cited by 2,804
- zero_addproof · cited by 2,366
- add_commproof · cited by 1,535
- one_smulproof · cited by 1,374
- add_assocproof · cited by 746
- smul_smulproof · cited by 360
- smul_addproof · cited by 263
- add_smulproof · cited by 204
- add_add_add_commproof · cited by 56
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.