Before revision: This linear model gives rise to explicit algebraic structure in terms of matrix Lie group representation of 2D self-motion, as well as explicit geometric structure where the self-motion is represented by the rotation of the vector. We connect the isotropic condition under the linear model to the hexagon grid patterns of the response maps of grid cells .
After revision: This linear model gives rise to explicit algebraic structure in terms of matrix Lie group of rotation, and establish the connection between the isotropic scaling condition and hexagon grid patterns of the response maps of grid cells .