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Theorems · Theorem · linear algebra

Matrix.mulVec_transpose

∀ {m : Type u_2} {n : Type u_3} {α : Type v} [inst : NonUnitalCommSemiring α] [inst_1 : Fintype m] (A : Matrix m n α)
  (x : m → α), A.transpose.mulVec x = Matrix.vecMul x A
Defined in
Mathlib.Data.Matrix.Mul
Cited by
3 results in Mathlib
Foundations
Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NonUnitalCommSemiringFintype
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matrix.mulVecLin_transpose · cited by 2Matrix.mulVecLin_transposeLDL.diag_eq_lowerInv_conj · cited by 1LDL.diag_eq_lowerInv_conjMatrix.mulVec_vecMul · cited by 0Matrix.mulVec_vecMulFintype · cited by 7736FintypeMatrix · cited by 4303MatrixMatrix.transpose · cited by 389Matrix.transposeMatrix.mulVec · cited by 267Matrix.mulVecMatrix.vecMul · cited by 148Matrix.vecMulNonUnitalCommSemiring · cited by 29NonUnitalCommSemiringdotProduct_comm · cited by 13dotProduct_commMatrix.mulVec_transposeCITED BYCITES

Cites7

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Cited by3

Results whose statement or proof uses this declaration.