For example, a typical boost and a typical rotation exponentiate as, exp ⁡ ⁡ ( − − i ξ ξ K 1 ) = ( cosh ⁡ ⁡ ξ ξ sinh ⁡ ⁡ ξ ξ 0 0 sinh ⁡ ⁡ ξ ξ cosh ⁡ ⁡ ξ ξ 0 0 0 0 1 0 0 0 0 1 ) , exp ⁡ ⁡ ( − − i θ θ J 1 ) = ( 1 0 0 0 0 1 0 0 0 0 cos ⁡ ⁡ θ θ − − sin ⁡ ⁡ θ θ 0 0 sin ⁡ ⁡ θ θ cos ⁡ ⁡ θ θ ) , symmetric and orthogonal, respectively.