I am reading The Principles of Quantum Mechanics 4th Ed by Paul Dirac, specifically where he introduces his own Bra-Ket notation. You can view this book as a google book. http://books.google.com.au/books?id...ce=gbs_ge_summary_r&cad=0#v=onepage&q&f=false On page 28 (on linear operators acting on kets and bras), after showing that "the conjugate complex of the product of two linear operators equals the product of the conjugate complexes of the factors in reverse order", He then says that "if ξ and η are real, in general ξη is not real". Can someone please explain or post a link to a reference showing how it can be that the product of two real linear operators is not necessarily real? OR, could it be a misprint?