  We show how in a matrix inflationary model in which there is a non-minimal
coupling between the matrix inflatons and gravity --hence dubbed
Non-$\MM$-flation-- some of the disadvantages of the minimal model can be
avoided. In particular, the number of D3 branes can be reduced substantially to
$\lesssim \mathcal{O}(100)$, which can alleviate the ``potential'' backreaction
problem of large number of D3 branes on the background geometry. This is
achieved by values of non-minimal coupling of order few hundred, which is much
smaller than that of Higgs Inflation. The prediction of the model in the
symmetry breaking part of the potential, which is a local attractor and can
support eternal inflation, is compatible with the latest PLANCK results. In
contrast to the minimal model, the spectator fields can partially or completely
reheat the universe, depending on the symmetry-breaking vacuum expectation
value and the non-minimal coupling parameter. We also comment on how the
presence of gauge species keep the UV cutoff at around the Planck scale in the
Einstein frame and, in contrast to the Higgs inflation, the problem of field
displacements beyond the cutoff does not occur.
