Hadamard Product Calculator
Calculate the element-wise (Hadamard) product of two matrices. The matrices must have the same dimensions.
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How Hadamard Product Works
The Hadamard product (also known as element-wise product) of two matrices A and B is denoted by A ⊙ B and is calculated by multiplying corresponding elements:
\[ (A \odot B)_{ij} = A_{ij} \times B_{ij} \]
Properties of Hadamard Product:
- Commutative: A ⊙ B = B ⊙ A
- Associative: (A ⊙ B) ⊙ C = A ⊙ (B ⊙ C)
- Distributive: A ⊙ (B + C) = A ⊙ B + A ⊙ C
- Identity element: A ⊙ J = A, where J is a matrix of ones
Applications:
- Signal processing
- Image processing
- Machine learning
- Neural networks
- Quantum computing