Theorems · Theorem · linear algebra
Matrix.mul_adjp_add_detp
∀ {n : Type u_1} {R : Type u_3} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommSemiring R]
(A : Matrix n n R), A * Matrix.adjp 1 A + Matrix.detp (-1) A • 1 = A * Matrix.adjp (-1) A + Matrix.detp 1 A • 1- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- mul_oneproof · cited by 3,885
- Unitsstatement · cited by 2,804
- MulZeroClass.mul_zeroproof · cited by 2,091
- add_commproof · cited by 1,535
- eq_or_neproof · cited by 1,117
- Matrix.extproof · cited by 540
- Matrix.one_apply_neproof · cited by 39
- Matrix.detpstatement and proof · cited by 37
- Matrix.one_apply_eqproof · cited by 35
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.detp_smul_add_adjpproof · cited by 1