Theorems · Theorem · linear algebra
Matrix.vecMul_transpose
∀ {m : Type u_2} {n : Type u_3} {α : Type v} [inst : NonUnitalCommSemiring α] [inst_1 : Fintype n] (A : Matrix m n α)
(x : n → α), Matrix.vecMul x A.transpose = A.mulVec x- Defined in
- Mathlib.Data.Matrix.Mul
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonUnitalCommSemiringFintype
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.
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Matrix.transposestatement and proof · cited by 389
- Matrix.mulVecstatement · cited by 267
- Matrix.vecMulstatement · cited by 148
- NonUnitalCommSemiringstatement and proof · cited by 29
- dotProduct_commproof · cited by 13
Cited by8
Results whose statement or proof uses this declaration.
- Matrix.mulVec_injective_iffproof · cited by 5
- Matrix.mulVec_injective_iff_isUnitproof · cited by 4
- Matrix.dotProduct_transpose_mulVecproof · cited by 3
- Matrix.vecMulLinear_transposeproof · cited by 1
- Matrix.ker_mulVecLin_transpose_mul_selfproof · cited by 1
- Algebra.traceMatrix_of_matrix_mulVecproof · cited by 1
- Matrix.det_smul_inv_vecMul_eq_cramer_transposeproof · cited by 1
- Matrix.vecMul_mulVecproof · cited by 0