<s>[INST] Vector, Matrix multiplication notation Given a vector $v=\begin{bmatrix} 1 \\ 2 \\ 3\end{bmatrix}$ and matrix $M=\begin{bmatrix} 1 & 2 & 3\\ 4 & 5 & 6 \\ 7 & 8 & 9\end{bmatrix}$ is there a standard notation for scaling each row of $M$ by the corresponding element of $v$. e.g.
$$\begin{bmatrix} 1 \\ 2 \\ 3\end{bmatrix} \circ_{Row} \begin{bmatrix} 1 & 2 & 3\\ 4 & 5 & 6 \\ 7 & 8 & 9\end{bmatrix} = \begin{bmatrix} 1 & 2 & 3\\ 8 & 10 & 12 \\ 21 & 24 & 27\end{bmatrix} = A$$
I could define it using $A_{ij} = v_i \cdot M_{ij}$ but would rather use an operator if there is one.
 [/INST] You could do it by
$$\begin{bmatrix} 1&0&0 \\0& 2&0 \\0&0& 3\end{bmatrix} 
\begin{bmatrix} 1 & 2 & 3\\ 4 & 5 & 6 \\ 7 & 8 & 9\end{bmatrix} = \begin{bmatrix} 1 & 2 & 3\\ 8 & 10 & 12 \\ 21 & 24 & 27\end{bmatrix}$$
easily.
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