The shear transformation of \(\RNrSpc{n}\) parallel to the hyperspace perpendicular to a nonzero vector \(\Vect{a}\), and with shear vector \(\Vect{s}\bot \Vect{a}\) is given by

\[\FnctnDAAT{S}{\RNrSpc{n}}{\RNrSpc{n}},\quad \FnctnOf{S}{\Vect{x}} = \Vect{x} + (\DotPr{ \Vect{a} }{ \Vect{x} })\cdot \Vect{s}\]