Hadamard Product Calculator (Element-wise Matrix Multiplication)

Your details

Both matrices must have the same number of rows and columns.
Enter each row separated by a semicolon (;) and values within a row separated by commas. Example for 2x2: "1, 2; 3, 4".
Must have the same dimensions as Matrix A. Example for 2x2: "5, 6; 7, 8".
Hadamard Product (A o B)
[[5, 12], [21, 32]]

The element-wise product matrix, C where c_ij = a_ij * b_ij.

Frobenius Norm of A5.4772
Frobenius Norm of B13.1909
Frobenius Norm of A o B40.4228
Commutative check (B o A)[[5, 12], [21, 32]]
Number of entries4
||A||_F5.4772
||B||_F13.1909
||A o B||_F40.4228

Hadamard product computed: A o B = [[5, 12], [21, 32]]

  • The Hadamard product multiplies 4 corresponding entry pairs to produce the result matrix.
  • Frobenius norms: ||A||_F = 5.4772, ||B||_F = 13.1909, ||A o B||_F = 40.4228.
  • The ratio ||A o B||_F / (||A||_F * ||B||_F) = 0.5595, which is always at most 1 by the Schur product theorem.
  • Because the Hadamard product is commutative, swapping A and B gives the identical result.

Next stepUse the step-by-step panel below to see each individual multiplication, or try a different matrix size to explore larger products.

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