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Recently the gaussian expansion method has been applied to investigate thedynamical generation of 4d space-time in the IIB matrix model, which is aconjectured nonperturbative definition of type IIB superstring theory in 10dimensions. Evidence for such a phenomenon, which is associated with thespontaneous breaking of the SO(10) symmetry down to SO(4), has been obtained upto the 7-th order calculations. Here we apply the same method to a simplifiedmodel, which is expected to exhibit an analogous spontaneous symmetry breakingvia the same mechanism as conjectured for the IIB matrix model. The results upto the 9-th order demonstrate a clear convergence, which allows us tounambiguously identify the actual symmetry breaking pattern by comparing thefree energy of possible vacua and to calculate the extent of ``space-time'' ineach direction.Comment: 23 pages, 20 figures, LaTe

Gaussian Expansion Analysis of a Matrix Model with the Spontaneous Breakdown of Rotational Symmetry