The Hadamard (element-wise) product is what most people first expect matrix multiplication to be. It is used in image masking, neural networks (gates in LSTMs), statistics and the Schur product theorem.
How to use the Hadamard Product Calculator
- Choose the matrix size – the matching grid of fields appears.
- Enter the entries row by row (a₁ b₁ c₁ is the first row, a₂ b₂ c₂ the second, and so on).
- Read the result; integer matrices give exact fractions.
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Corresponding entries are multiplied. Both matrices must have the same dimensions.
Formula
(A ∘ B)ᵢⱼ = aᵢⱼ × bᵢⱼ
Worked example
Inputs — Matrix size (rows × columns): 2 × 2; a₁: 4; b₁: 1; a₂: 1; b₂: 3; B: x₁: 1; B: y₁: 2; B: x₂: 0; B: y₂: 1.
Results — A ∘ B = ⎡ 4 2 ⎤
⎣ 0 3 ⎦.
Key terms
- Hadamard product
- Element-wise matrix multiplication.
Frequently asked questions
Is the Hadamard product the same as matrix multiplication?
No – it multiplies entry by entry.
Do the matrices need the same size?
Yes.
Is it commutative?
Yes, A ∘ B = B ∘ A.
What is the identity for the Hadamard product?
The matrix of all ones.