  We generalize a construction of coherent state operators describing various
giant graviton branes. We enlarge the coherent state parameters, by including
complementary coherent state parameters, to describe a system of dual giants
and giants. One of the advantages of using complementary coherent state
parameters is that they have rich sub-block structures that record different
type of giant gravitons or wrapped branes. The coherent state parameters are
further packaged into supermatrix, to construct special coherent states, which
encode information of both giants and dual giants. We add strings onto the
coherent state operators. The string-added states capture near-BPS states.
Hence the constructions of BPS coherent state operators are also useful for
analyzing near-BPS states. The coherent state representation, auxiliary
integrals, as well as auxiliary susy integrals, facilitate the computations
efficiently. We describe multi-matrix operators and BPS states, and unify some
classes of operators. Finally, reduced coherent states as well as their
fermionic counterparts are discussed.
