Theorems · Theorem · linear algebra
Matrix.det_conjTranspose
∀ {m : Type u_1} [inst : DecidableEq m] [inst_1 : Fintype m] {R : Type v} [inst_2 : CommRing R] [inst_3 : StarRing R]
(M : Matrix m m R), M.conjTranspose.det = star M.det- Cited by
- 7 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- StarRingstatement and proof · cited by 1,686
- Star.starstatement and proof · cited by 1,082
- starRingEndproof · cited by 671
- Matrix.detstatement · cited by 665
- Matrix.transposeproof · cited by 389
- Matrix.conjTransposestatement · cited by 202
- Matrix.det_transposeproof · cited by 51
- RingHom.map_detproof · cited by 41
Cited by7
Results whose statement or proof uses this declaration.
- LinearMap.normDet_eq_zero_iff_ker_ne_botproof · cited by 5
- Matrix.conjTranspose_nonsing_invproof · cited by 5
- Matrix.det_of_mem_unitaryproof · cited by 4
- Matrix.IsHadamard.det_mul_star_detproof · cited by 3
- Matrix.IsHadamard.of_mul_conjTransposeproof · cited by 1
- ContinuousLinearMap.normDet_sqproof · cited by 1
- LinearMap.normDet_sq_eq_det_gramproof · cited by 0