Hadamard Product

linear-algebra

Definition

Hadamard Product

Let $x,y\in F^n$ be vectors over a field $F$. The Hadamard product (entrywise product) is the operation

$$\odot :F^n\times F^n\to F^n.$$

Einstein Notation: $(x\odot y{)}_i=x_i{y}_i\in F^n$

Unlike the dot product, no sum is taken — the index $i$ is kept, so the output is a vector, not a scalar.