  Recently, S. Murthy has proposed a convergent expansion of free partition
functions and superconformal indices of finite-$N$ purely adjoint gauge
theories based on a Fredholm determinant expansion. This expansion has been
dubbed the giant graviton expansion and takes the form of an infinite series of
corrections to the $N=\infty$ result, with the $m^\text{th}$ correction being
of order $e^{-mN}$. We show that this expansion can be reproduced using
eigenvalue instantons in unitary matrix integrals. This perspective allows us
to get the giant graviton expansion proposed by S. Murthy without the
intermediate step of the Hubbard Stratonovich transformation.
