# Hadamard product of matrices #

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This file defines the Hadamard product matrix.hadamard and contains basic properties about them.

## Main definition #

• matrix.hadamard: defines the Hadamard product, which is the pointwise product of two matrices of the same size.

## Notation #

• ⊙: the Hadamard product matrix.hadamard;

## Tags #

def matrix.hadamard {α : Type u_1} {m : Type u_4} {n : Type u_5} [has_mul α] (A B : n α) :
n α

matrix.hadamard defines the Hadamard product, which is the pointwise product of two matrices of the same size.

Equations
@[simp]
theorem matrix.hadamard_apply {α : Type u_1} {m : Type u_4} {n : Type u_5} [has_mul α] (A B : n α) (i : m) (j : n) :
A.hadamard B i j = A i j * B i j
theorem matrix.hadamard_comm {α : Type u_1} {m : Type u_4} {n : Type u_5} (A B : n α)  :
theorem matrix.hadamard_assoc {α : Type u_1} {m : Type u_4} {n : Type u_5} (A B C : n α) [semigroup α] :
theorem matrix.hadamard_add {α : Type u_1} {m : Type u_4} {n : Type u_5} (A B C : n α) [distrib α] :
theorem matrix.add_hadamard {α : Type u_1} {m : Type u_4} {n : Type u_5} (A B C : n α) [distrib α] :
@[simp]
theorem matrix.smul_hadamard {α : Type u_1} {m : Type u_4} {n : Type u_5} {R : Type u_6} (A B : n α) [has_mul α] [ α] [ α] (k : R) :
@[simp]
theorem matrix.hadamard_smul {α : Type u_1} {m : Type u_4} {n : Type u_5} {R : Type u_6} (A B : n α) [has_mul α] [ α] [ α] (k : R) :
@[simp]
theorem matrix.hadamard_zero {α : Type u_1} {m : Type u_4} {n : Type u_5} (A : n α)  :