How do I solve the following?
F^T e' = \vec{0} , where $F$ is a square 3x3 matrix, and $e$ is a 3-space vector.
My ansatz
If I prepend $F^{-T}$ on both sides I get:
F^{-T} F^T e'= F^{-T} \vec{0}
Which is the trivial case e' = \vec{0}.
Does a solution from knowing only this equation exist? How would I find it? (Also, how would you google such a question?)
I am trying to solve a problem in computer vision. F is the fundamental matrix, and e' the epipole. I got this from p.246 of Hartley & Zisserman, Multiple View Geometry. By chance, that chapter is available online: http://www.robots.ox.ac.uk/~vgg/hzbook/hzbook2/HZepipolar.pdf
EDIT: This question originally revealed that F is of rank 2. Out of interest, I would still like to know, how to solve this if the rank was 3. (And not using Matlab...)