Ahh of course, use the rotation matrix twice. This gets me B proportional to A* if I use the normal (real valued) rotation matrix. Is there a complex version that will get me B proportional A?
Homework Statement
Two plane gravitational waves with TT (transverse-traceless) amplitudes, ##A^{\mu\nu}## and ##B^{\mu\nu}##, are said to have orthogonal polarizations if ##(A^{\mu\nu})^*B_{\mu\nu}=0##, where ##(A^{\mu\nu})^*## is the complex conjugate of ##A^{\mu\nu}##. Show that a 45 degree...