Is there a standard matrix operation that multiplies the elements of each matrix together based only on their position? For example,
$$\begin{pmatrix}1&2&3\\4&5&6\end{pmatrix}\ast\begin{pmatrix}1&0&1\\0&1&0\end{pmatrix} = \begin{pmatrix}1 & 0 & 3\\0 & 5 & 0\end{pmatrix}.$$