the extra dimensions that appears naturally in typical solutions can be viewed as a realization of intersecting D-branes. In particular, we show that the Dirac zero modes appear with localized wave functions when the dimensionality of the D-branes is chosen appropriately. Section \[conlusion\] is devoted to a summary and discussions.

Generating classical solutions {#sec:classicalsolution}
==============================

In this section, after a brief review of the type IIB matrix model, we explain how we generate its classical solutions numerically.

the type IIB matrix model and its classical solutions
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The action of the type IIB matrix model is given as [@Ishibashi:1996xs] $$\begin{aligned}
S&=S_\mathrm{b} + S_\mathrm{f}\ , 
\label{S_tot}
\\
S_\mathrm{b} &= -\frac{1}{4g^2} 
{\mbox{Tr}}{\left( {{\left[ A^M, A^N \right]}} {{\left[ A_M, A_N \right]}} \right)} \ , 
\label{S_b}
\\
S_\mathrm{f} &= -\frac{1}{2g^2} 
{\mbox{Tr}}{\left( \Psi_{\alpha} (\mathcal{C} \Gamma^M)_{\alpha\beta} 
{{\left[ A_M, \Psi_{\beta} \right]}} \right)} \ ,
\label{S_f}\end{aligned}$$ where $A^M \ (M=0,\ldots,9)$ and $\Psi_{\alpha}\ (\alpha=1,\ldots,16)$ are $N \times N$ traceless Hermitian matrices, while $\Gamma^M$ and $\mathcal{C}$ are the gamma matrices and the charge conjugation matrix in ten dimensions after the Weyl projection. The indices $M$ and $N$ are raised and lowered by using the metric $\eta={\rm diag}(-1,1, \ldots , 1)$. The action is invariant under the SO(9,1) transformation, where $A^M$ 