Hadamard product

tags
Linear Algebra

This is an element wise product between two vectors or matrices.

It is quite simply the element-wise produce between two matrices: \(\mathcal{A}, \mathcal{B}: n \times m\).

\begin{align*} \left[\begin{array}{cc} {A_{11}} & {A_{12}} \\\
{A_{21}} & {A_{22}} \\\
{A_{31}} & {A_{32}} \end{array}\right] \odot \left[\begin{array}{cc} {B_{11}} & {B_{12}} \\\
{B_{21}} & {B_{22}} \\\
{B_{31}} & {B_{32}} \end{array}\right] &= \left[\begin{array}{ll} {A_{11}B_{11}} & {A_{12}B_{12}} \\\
{A_{21}B_{21}} & {A_{22}B_{22}} \\\
{A_{31}B_{31}} & {A_{32}B_{32}} \end{array}\right] \\\
\left[\begin{array}{cc} {2} & {1} \\\
{3} & {0} \\\
{0} & {4} \end{array}\right] \odot \left[\begin{array}{cc} {1} & {2} \\\
{-3} & {1} \\\
{1} & {2} \end{array}\right] &= \left[\begin{array}{ll} {2} & {2} \\\
{-9} & {0} \\\
{0} & {8} \end{array}\right] \end{align*}