The schwarz inequality says that for any two kets v) and w) in a complex inner product space, viw)< ivi|w\, where the norm is defined by |v = (v|v). the proof is given on page 17 of shankar; write it out and find under what circumstances equality holds. use this to prove the triangle inequality for the norm of |v + w) = |v) + |w): and show that equality holds if and only if |w) = a|v) where a is a non-negative real number. hint: start with |v + w2, and use the property of complex numbers re(z)