The infinitesimal strain tensor is defined as ε ε = 1 2 [ ∇ ∇ u + ( ∇ ∇ u ) T ] Therefore the displacement gradient can be expressed as ∇ ∇ u = ε ε + W where W := 1 2 [ ∇ ∇ u − − ( ∇ ∇ u ) T ] The quantity W is the infinitesimal rotation tensor or infinitesimal angular displacement tensor (related to the infinitesimal rotation matrix). This tensor is skew symmetric. For infinitesimal deformations the scalar components of W satisfy the condition | W i j | ≪ ≪ 1 . Note that the displacement gradient is small only if both the strain tensor and the rotation tensor are infinitesimal.