TOPICS
Search

Hadamard Matrix Product

The Hadamard matrix product, also called the entrywise product or Schur product, of two m×n matrices A=(a_(ij)) and B=(b_(ij)) is the m×n matrix

A degreesB=(a_(ij)b_(ij)).

Unlike ordinary matrix multiplication, the Hadamard matrix product multiplies corresponding entries and is defined only for matrices of the same dimensions. It is commutative and associative, and its identity element is the unit matrix having every entry equal to 1 (Horn and Johnson 1991).

See also

Hadamard Product, Matrix Multiplication, Unit Matrix

Explore with Wolfram|Alpha

References

Horn, R. A. and Johnson, C. R. "The Hadamard Product." Ch. 5 in Topics in Matrix Analysis. Cambridge, England: Cambridge University Press, pp. 298-381, 1991. https://doi.org/10.1017/CBO9780511840371.006.

Cite this as:

Weisstein, Eric W. "Hadamard Matrix Product." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HadamardMatrixProduct.html

Subject classifications