Source: cirosantilli/the-orthogonal-group-is-the-group-of-all-matrices-with-orthonormal-rows-and-orthonormal-columns
= The orthogonal group is the group of all matrices with orthonormal rows and orthonormal columns
Or equivalently, the set of rows is <orthonormal>, and so is the set of columns. TODO proof that it is equivalent to <the orthogonal group is the group of all matrices that preserve the dot product>.