“Show that |v><v| is Hermitian.”
“Calculate (|v><v|)2.”
“Calculate (|v><v|)(|w><w|).”
This SWBQ is intended to help students become familiar with the properties of projection operators.
Students should consider each question one at a time, followed by a brief class discussion to ensure students get the relevant points. In particular, (|v><v|)2 = (|v><v|) and (|v><v|)(|w><w|) = 0 as a way to building the matrix decomposition theorem.