I'm having difficulty understanding the geometry of a spacetime split as it applies to geometric algebra. I understand vectors, bivectors, and trivectors and I understand geometric products and wedge products. My impression is that a spacetime split lets you decompose an electromagnetic field into an E and B for a given inertial frame. Is this correct? Can someone clue me in on the geometry here? I've been studying from Hestenes and Doran & Lasenby.