Hadamard product
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- 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*}