Theorems · Theorem · linear algebra
Matrix.transpose_mul
∀ {l : Type u_1} {m : Type u_2} {n : Type u_3} {α : Type v} [inst : AddCommMonoid α] [inst_1 : CommMagma α]
[inst_2 : Fintype n] (M : Matrix m n α) (N : Matrix n l α), (M * N).transpose = N.transpose * M.transpose- Defined in
- Mathlib.Data.Matrix.Mul
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Matrix.extproof · cited by 540
- Matrix.transposestatement · cited by 389
- CommMagmastatement and proof · cited by 57
- dotProduct_commproof · cited by 13
Cited by14
Results whose statement or proof uses this declaration.
- Matrix.adjugate_mulproof · cited by 6
- Matrix.trace_mul_commproof · cited by 5
- Matrix.adjp_mul_apply_eqproof · cited by 1
- Matrix.adjp_mul_apply_neproof · cited by 1
- det_traceForm_ne_zeroproof · cited by 1
- Matrix.lie_transposeproof · cited by 1
- Matrix.IsHadamard.transposeproof · cited by 1
- RootPairing.Base.exists_cartanMatrix_diagaonal_mul_posDefproof · cited by 1
- Matrix.isAdjointPair_equivproof · cited by 1
- Matrix.mem_subfield_of_mul_eq_one_of_mem_subfield_leftproof · cited by 1
- Matrix.isSymm_transpose_mul_selfproof · cited by 0
- Matrix.transpose_mem_unitaryGroup_iffproof · cited by 0