1. What is the Hadamard Product?

The Hadamard product (also known as the element-wise product) is a binary operation that takes two matrices of the same dimensions and produces another matrix where each element is the product of the corresponding elements from the original matrices.

2. How Does the Calculator Work?

The calculator implements the Hadamard product formula:

Where:

• \( A \) — First input matrix
• \( B \) — Second input matrix (must have same dimensions as A)
• \( \circ \) — Hadamard product operator
• \( i,j \) — Row and column indices

Explanation: The calculator parses the input matrices, verifies their dimensions match, then computes the element-wise product.

3. Importance of Hadamard Product

Details: The Hadamard product is widely used in machine learning, signal processing, and quantum computing. It's particularly important in neural networks for attention mechanisms and gating operations.

4. Using the Calculator

Tips: Enter matrices in comma-separated format (rows separated by semicolons). For example:
Matrix A: 1, 2, 3; 4, 5, 6
Matrix B: 2, 0, 1; 1, 2, 3
Result: 2, 0, 3; 4, 10, 18

5. Frequently Asked Questions (FAQ)

Q1: How is Hadamard product different from matrix multiplication?
A: Hadamard product is element-wise while matrix multiplication involves dot products of rows and columns.

Q2: What Python libraries support Hadamard product?
A: NumPy (using * operator or numpy.multiply()), TensorFlow (tf.multiply()), and PyTorch (torch.mul()).

Q3: Can I multiply matrices of different sizes?
A: No, Hadamard product requires matrices of identical dimensions.

Q4: What are common applications of Hadamard product?
A: Image processing filters, attention mechanisms in transformers, and activation functions in neural networks.

Q5: Is Hadamard product commutative?
A: Yes, A∘B = B∘A for all matrices of the same size.