# How does one write the following expression D_(jk)(r_k delta_(ij)−r_i delta_(jk)−r_j delta_(ik)) in matrix notation? Is this just bb(D(r xx I))?

How does one write the following expression
${D}_{jk}\left({r}_{k}{\delta }_{ij}-{r}_{i}{\delta }_{jk}-{r}_{j}{\delta }_{ik}\right)$
in matrix notation? Is this just
$\mathbf{\text{D}}\left(\mathbf{\text{r}}×\mathbf{\text{I}}\right)$?
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Edward Chase
The given expression in matrix notation should be:

By applying the Kronecker Delta we have:
${D}_{jk}\left({r}_{k}{\delta }_{ij}-{r}_{i}{\delta }_{jk}-{r}_{j}{\delta }_{ik}\right)\phantom{\rule{0ex}{0ex}}={D}_{jk}{r}_{k}{\delta }_{ij}-{D}_{jk}{r}_{i}{\delta }_{jk}-{D}_{jk}{r}_{j}{\delta }_{ik}\phantom{\rule{0ex}{0ex}}={D}_{ik}{r}_{k}-{D}_{kk}{r}_{i}-{D}_{ji}{r}_{j}\phantom{\rule{0ex}{0ex}}$
I was not able to find a cross product (Levi-Civita expression) from the given Kronecker Detla Expression.