Im confused about how mathematically this works. If E is 3x3 and x is 3x1, then l' should be a 3x1 vector. How does this map to a line; shouldn't it be a point?
mpotoole
Yes! $l'$ is a 3x1 vector, which is defined in more detail on this slide. In short, all homogeneous points $x'$ on the line $l'$ will satisfy the equation $x'^T l' = 0$. So even though both $x'$ and $l'$ both have the same dimensions, they should not be interpreted in the same way.
Im confused about how mathematically this works. If E is 3x3 and x is 3x1, then l' should be a 3x1 vector. How does this map to a line; shouldn't it be a point?
Yes! $l'$ is a 3x1 vector, which is defined in more detail on this slide. In short, all homogeneous points $x'$ on the line $l'$ will satisfy the equation $x'^T l' = 0$. So even though both $x'$ and $l'$ both have the same dimensions, they should not be interpreted in the same way.