I have a linear transformation $ A = I - 2vv^\top $ where $ v $ is n dimensional unit vector. I'm looking for a geometrical meaning for the transformation A. I can write $ A $ as $ A = (I - vv^\top ) - vv^\top $ so it is a projection onto the nullspace of $v$ minus the projection onto $v$. Any other geometrical insight I can gain for this transformation ?
Thanks!