Theorems · Theorem · linear algebra
Matrix.conjTranspose_mul
∀ {l : Type u_1} {m : Type u_2} {n : Type u_3} {α : Type v} [inst : Fintype n] [inst_1 : NonUnitalNonAssocSemiring α]
[inst_2 : StarRing α] (M : Matrix m n α) (N : Matrix n l α), (M * N).conjTranspose = N.conjTranspose * M.conjTranspose- Cited by
- 9 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Finset.sumproof · cited by 5,195
- Matrixstatement and proof · cited by 4,303
- Finset.univproof · cited by 3,473
- Finset.sum_congrproof · cited by 2,323
- StarRingstatement and proof · cited by 1,686
- Star.starproof · cited by 1,082
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- Matrix.extproof · cited by 540
- Matrix.conjTransposestatement · cited by 202
- StarMul.star_mulproof · cited by 72
- star_sumproof · cited by 9
Cited by9
Results whose statement or proof uses this declaration.
- LinearMap.normDet_eq_norm_det_toMatrix_rangeRestrictproof · cited by 8
- Matrix.isHermitian_conjTranspose_mul_mulproof · cited by 3
- Matrix.conjTranspose_mul_self_mul_eq_zeroproof · cited by 2
- Matrix.isHermitian_conjTranspose_mul_selfproof · cited by 2
- Matrix.isHermitian_mul_conjTranspose_selfproof · cited by 1
- Matrix.mul_self_mul_conjTranspose_eq_zeroproof · cited by 1
- Matrix.schur_complement_eq₁₁proof · cited by 1
- Matrix.isHermitian_mul_mul_conjTransposeproof · cited by 0
- Matrix.schur_complement_eq₂₂proof · cited by 0