I have a question regarding the calculation of hodge stars of $2$-forms in $4$-space. I am having trouble understanding the six expressions, such as $*(dx\wedge dy) = dz\wedge dt$ and $*(dz\wedge dx) = -dy\wedge dt$. I am simply confused on how to apply to definition. The six expressions and the definition can be found on this webpage:
http://unapologetic.wordpress.com/2012/03/07/minkowski-space/