Cosider the two following matrices: \begin{align} E=\begin{bmatrix} e_{11}\;\; e_{12} \\ e_{21}\;\; e_{22} \\ \end{bmatrix} \end{align} and \begin{align} X=\begin{bmatrix} x_{11}\;\; x_{12} \\ x_{21}\;\; x_{22} \\ \end{bmatrix} \end{align} I want to divide each element with each other. So I get the following matrix (let's call that $K$): \begin{align} K=\begin{bmatrix} e_{11}/x_{11}\;\; e_{12}/x_{12} \\ e_{21}/x_{21}\;\; e_{22}/x_{22} \\ \end{bmatrix} \end{align} How do I wrote that as an equation. My best guess is: \begin{align} K=E \circ X^{-1} \end{align} Where I use the Hadamard product. But I am not sure whether this is correct.
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make sure that $ x_{ij} \neq 0$ for all $i,j$ – Riquelme Aug 29 '19 at 14:26
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3Close. However, $X^{-1}$ generally refers to the multiplicative inverse of the matrix where the multiplication here is the usual multiplication. What you want is the hadamard multiplicative inverse of $X$., denoted as $X^{\circ -1}$ – JMoravitz Aug 29 '19 at 14:27
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As JMoravitz points out in the comments, apparently there is somewhat standard notation for Hadamard multiplicative inverse.
No matter how you write it, though, the operation you're trying to do is so unusual compared to the standard matrix inverse that I would add a note clearly explaining to the reader the notation.
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