Aside: I&#x27;m not signed up for the site (not interested in tying that login to other accounts), but I wanted to comment that luisb&#x27;s explanation of Eq. (13) seems to miss the point a little. That equation doesn&#x27;t need to be <i>derived</i> from Eq. (4). Instead, Eq. (13) is just a statement that any antisymmetric 3x3 matrix can always be recharacterized as a (pseudo)vector &quot;times&quot; the totally antisymmetric Levi-Civita symbol epsilon_{ijk}. As the text says, Eq. (13) is the <i>definition</i> of H. Only after we&#x27;ve defined what H is can we then use Eq. (4) to provide a definition of E.