  In semidefinite programming the dual may fail to attain its optimal value and
there could be a duality gap, i.e., the primal and dual optimal values may
differ. In a striking paper, Ramana proposed a polynomial size extended dual
that does not have these deficiencies and yields a number of fundamental
results in complexity theory. In this work we walk the reader through a concise
and self-contained derivation of Ramana's dual, relying mostly on elementary
linear algebra.
