There is a transformation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\vec{E}\times\left(\nabla\times\vec{E}\right)=

\vec{k}_{i}\epsilon_{ijk}E_j\left(\nabla\times\vec{E}\right)_k=

\vec{k}_{i}\epsilon_{jk}E_j\epsilon_{klm}\nabla_l E_m=

\vec{k}_i\epsilon_{ijk}\epsilon_{klm}E_j\nabla_l E_m

=\vec{k}_i\left(\delta_{il}\delta_{jm}-\delta_{im}\delta_{jl}\right)E_j\nabla_l E_m= [/tex]

[tex]=\vec{k}_i\delta_{il}\delta_{jm}E_j\nabla_l E_m-\vec{k}_i\delta_{im}\delta_{jl}E_j\nabla_l E_m=\vec{k}_i jE_j\nabla_i E_j-\vec{k}_i E_j\nabla_j E_i={{1}\over{2}}\nabla E^2-\left(\vec{E}\nabla\right)\vec{E} [/tex]

I think it is connected somehow to matrixes, but I do not get it at all. The way how it is done looks quite nice so maybe it is worth to learn this method. Can someone just help me with understanding it?

PS. Sorry if I posted it in a wrong forum, i just do not know where I am supposed to write it...

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Transformation of some formula

Loading...

Similar Threads for Transformation formula |
---|

I Intuitive Linear Transformation |

I What is difference between transformations and automorphisms |

I Solutions to equations involving linear transformations |

**Physics Forums - The Fusion of Science and Community**