Theorems · Theorem · linear algebra
Matrix.detp_transpose
∀ {n : Type u_1} {R : Type u_3} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommSemiring R] (s : ℤˣ)
(A : Matrix n n R), Matrix.detp s A.transpose = Matrix.detp s A- Cited by
- 5 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Unitsstatement and proof · cited by 2,804
- Equiv.Permproof · cited by 1,375
- Matrix.transposestatement · cited by 389
- Equiv.symm_apply_applyproof · cited by 320
- Equiv.Perm.signproof · cited by 138
- Matrix.detpstatement · cited by 37
- Equiv.invproof · cited by 23
- Equiv.Perm.ofSignproof · cited by 21
Cited by5
Results whose statement or proof uses this declaration.
- Matrix.isDetpBalanced_transpose_iffproof · cited by 2
- Matrix.adjp_mul_apply_eqproof · cited by 1
- Matrix.detp_eq_of_col_eqproof · cited by 1
- Matrix.adjp_none_someproof · cited by 0
- Matrix.detp_eq_of_col_eq_zeroproof · cited by 0