close to $1/3$ as far as we use the same Gaussian distribution for all the elements of $X_\mu$, $Y_a$ and $M$ in the initial configuration. A solution that belongs to the above class (\[eq: correspondence\_MY\]) is obtained without being trapped in a local minimum when the value of the parameter $\zeta$ lies within the range $$\label{eq:mass_region} 
0.1 \lesssim \zeta \lesssim 0.5 \ .$$

Space-time structure in the (3+1) dimensions {#Sec:analysis_X}
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Using the method described in the previous section, we obtain classical solutions of the type IIB matrix model within the ansatz (\[eq: ansatz of A\]). By generating the initial configurations randomly, we can obtain as many solutions as we wish satisfying –. In this section, we focus on the matrices $X_{\mu}$ in (\[eq: ansatz of A\]), which represent the structure of the (3+1)-dimensional space-time.

band-diagonal structure {#SS:Config_X}
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Using the SU($N$) symmetry with $U=g \otimes \mathbf{1}$, $g \in \mathrm{SU}(N_{\rm X})$, we can choose a basis in which $X_{0}$ is diagonal with its elements arranged in the ascending order. In Fig. \[fig:X0\], we show the eigenvalues $\alpha_{p}\ (p=1,2,\ldots,N_{\rm X})$ of $X_0$ for a typical solution with $N_{\rm X} = 64$. We find that the eigenvalues are almost uniformly distributed, which 