We derive a Kontsevich-type matrix model for the c = 1 string directly
from the W-infinity solution of the theory, The model that we obtain
is different from previous proposals, which are proven to be incorrect
. Our matrix model contains the Penner and Kontsevich cases, and we st
udy its quantum effective action, The simplicity of our model leads to
an encouraging interpretation in the context of background-independen
t non-critical string field theory.