Hadamard product (matrices)

In mathematics, the Hadamard product (also known as the Schur product or the entrywise product) is a binary operation that takes two matrices of the same dimensions, and produces another matrix where each element ij is the product of elements ij of the original two matrices. It should not be confused with the more common 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, and unlike the matrix product it is also commutative.

For two matrices, ${\displaystyle A,B}$, of the same dimension, ${\displaystyle m\times n}$, the Hadamard product, ${\displaystyle A\circ B}$, is a matrix, of the same dimension as the operands, with elements given by

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