The state of pure shear

In classical continuum mechanics a stare of pure shear is defined as one fo r which there is some orthonormal basis relative to which the normal compon ents of the Cauchy stress tensor vanish. An equivalent characterization is that the trace of the Cauchy stress tensor must vanish. We give an elementa ry but complete discussion of this fundamental theorem here from both the g eometric and algebraic points of view.