Theorems · Theorem · linear algebra

Matrix.dotProduct_transpose_mulVec

∀ {m : Type u_2} {n : Type u_3} {α : Type v} [inst : NonUnitalCommSemiring α] [inst_1 : Fintype m] [inst_2 : Fintype n]
  (A : Matrix m n α) (x : n → α) (y : m → α), x ⬝ᵥ A.transpose.mulVec y = y ⬝ᵥ A.mulVec x

Bilinear form identity: x ⬝ᵥ Aᵀ *ᵥ y = y ⬝ᵥ A *ᵥ x for commutative semirings.

Defined in

Mathlib.Data.Matrix.Mul

Cited by

3 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonUnitalCommSemiringFintypeFintype