In PyTorch, element-wise matrix multiplication (the Hadamard product) is a binary operation that takes in two matrices of the same dimensions and returns a matrix of the multiplied corresponding elements.
This operation can be thought of as a “naive matrix multiplication” and is different from the matrix product. The element-wise matrix multiplication is associative and distributive. Unlike the matrix product, it is also commutative.
For two matrices A and B of the same dimension m × n, the element-wise matrix multiplication A ⊙ B is a matrix of the same dimension as the operands, with elements given. For example, the element-wise matrix multiplication for two arbitrary 3 × 3 matrices is:
For matrices of different dimensions (m × n and p × q, where m ≠ p or q), the element-wise matrix multiplication is undefined. Given two tensors x and y, you can simply use x * y or torch.mul(x, y).
import torch
x = torch.tensor([[4,1,5],
[5,3,7],
[8,4,2]])
y = torch.tensor([[2,3,7],
[4,9,1],
[2,7,3]])
torch.mul(x, y)
x * yResult:
tensor([[ 8, 3, 35],
[20, 27, 7],
[16, 28, 6]])The @ operator performs matrix multiplication. If A and B are NumPy arrays, then A @ B is equivalent to np.matmul(A, B). Many other libraries, like TensorFlow, and PyTorch, support the @ operator as well. However, you cannot use @ on pure Python arrays (i.e., lists of lists).