Theorems · Theorem · linear algebra

Matrix.dotProduct_vecMul_transpose

∀ {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), Matrix.vecMul x A.transpose ⬝ᵥ y = Matrix.vecMul y A ⬝ᵥ 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

0 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonUnitalCommSemiringFintypeFintype