Hadamard product (matrices)

In mathematics, the Hadamard product (also known as the element-wise product, entrywise product^[1]^{: ch. 5} or Schur product^[2]) 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 as a "naive matrix multiplication" and is different from the matrix product. It is attributed to, and named after, either French mathematician Jacques Hadamard or German mathematician Issai Schur.

The Hadamard product is associative and distributive. Unlike the matrix product, it is also commutative.^[3]

^ Cite error: The named reference HornJohnson was invoked but never defined (see the help page).
^ Davis, Chandler (1962). "The norm of the Schur product operation". Numerische Mathematik. 4 (1): 343–44. doi:10.1007/bf01386329. S2CID 121027182.
^ Million, Elizabeth (April 12, 2007). "The Hadamard Product" (PDF). buzzard.ups.edu. Retrieved September 6, 2020.

[HornJohnson-1] Cite error: The named reference HornJohnson was invoked but never defined (see the help page).

[2] Davis, Chandler (1962). "The norm of the Schur product operation". Numerische Mathematik. 4 (1): 343–44. doi:10.1007/bf01386329. S2CID 121027182.

[:1-3] Million, Elizabeth (April 12, 2007). "The Hadamard Product" (PDF). buzzard.ups.edu. Retrieved September 6, 2020.

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