How to add bracket under a matrix; two matrix in the same row

Question

matrix:

\begin{bmatrix}
    0 & 0 & 0 & 0 & 0& 0 &\cdots \\
    0 & 0 & 0 &0 & 0 & 0 &\cdots\\
    x_{i,1} &0 &0 & 0 & 0&0 &\cdots \\
    0&x_{i,2}&x_{i,1} &0 & 0&0 &\cdots \\
    0&0& 0 &x_{i,3} &x_{i,2} &x_{i,1} &\cdots\\
    \vdots & \vdots & \vdots &\vdots  &\vdots & \vdots  &\ddots\\
    \end{bmatrix} 

\begin{bmatrix}
    0 & 0 & 0 & 0 &\cdots \\
    0 & 0  & 0 &0 &\cdots \\
    \Delta x_{i,2} &0  &0 &0 &\cdots \\
    0&\Delta  x_{i,3} &0& 0  & \cdots\\
    0& 0 & \Delta x_{i,4}&0 &\cdots\\
    \vdots & \vdots & \vdots  & \vdots  &\ddots
    \end{bmatrix}

I got to know how to add embrace under one matrix from this forum. I hope to generate two matrices with different underneath text. It would be better if there is a larger space between these two matrices. Thanks a million.

Answer 1

With use of the \underbrace{<your matrix>}_{\text{<your text>}}:

\documentclass{article}
\usepackage{amsmath}

\begin{document}
\[
\underbrace{\begin{bmatrix}   % <---
    0 & 0 & 0 & 0 & 0& 0 &\cdots \\
    0 & 0 & 0 &0 & 0 & 0 &\cdots\\
    x_{i,1} &0 &0 & 0 & 0&0 &\cdots \\
    0&x_{i,2}&x_{i,1} &0 & 0&0 &\cdots \\
    0&0& 0 &x_{i,3} &x_{i,2} &x_{i,1} &\cdots\\
    \vdots & \vdots & \vdots &\vdots  &\vdots & \vdots  &\ddots\\
    \end{bmatrix}}_{\text{DIF equation}}
%
\underbrace{\begin{bmatrix}   % <---
    0 & 0 & 0 & 0 &\cdots \\
    0 & 0  & 0 &0 &\cdots \\
    \Delta x_{i,2} &0  &0 &0 &\cdots \\
    0&\Delta  x_{i,3} &0& 0  & \cdots\\
    0& 0 & \Delta x_{i,4}&0 &\cdots\\
    \vdots & \vdots & \vdots  & \vdots  &\ddots
    \end{bmatrix}}_{\text{LEV equation}}
\]
\end{document}