  We describe a new way of rewriting the partition function of scalar field
theory on fuzzy complex projective spaces as a solvable multitrace matrix
model. This model is given as a perturbative high-temperature expansion. At
each order, we present an explicit analytic expression for most of the arising
terms; the remaining terms are computed explicitly up to fourth order. The
method presented here can be applied to any model of hermitian matrices. Our
results confirm constraints previously derived for the multitrace matrix model
by Polychronakos. A further implicit expectation about the shape of the
multitrace terms is however shown not to be true.
