  In this paper, we compute uncertainty relations for non-commutative space and
obtain a better lower bound than the standard one obtained from Heisenberg's
uncertainty relation. We also derive the reverse uncertainty relation for
product and sum of uncertainties of two incompatible variables for one linear
and another non-linear model of the harmonic oscillator. The non-linear model
in non-commutating space yields two different expressions for Schr\"odinger and
Heisenberg uncertainty relation. This distinction does not arise in commutative
space, and even in the linear model of non-commutative space.
