How to draw this matrix

Here is a proposition with nicematrix. It's difficult to have a good result because of the width of the elements a_{n,n-d_1+1} and a_{n-d_u+1,n} which are much wider than the other elements.

documentclass{article}
usepackage{nicematrix,tikz}

begin{document}

NiceMatrixOptions
  {
    xdots = 
     {
       color = gray ,
       shorten = 3pt ,
     }
  }

$begin{pNiceMatrix}[columns-width=8mm,first-row,first-col]
& Hdotsfor[line-style={solid,<->},color=black]{4}^{d_u} 
Vdotsfor[line-style={solid,<->},color=black]{4}_{d_1}
& a_{11} & a_{12} & Cdots & a_{1d_u} & 0 & Cdots & & 0 [1.5mm]
& a_{21} & a_{22} &  &         &   & &   & Vdots [1.5mm]
& Vdots &  & Ddots &        &    & Ddots  &  Ddots &   [1.5mm]
& a_{d_11}&  &    &        &    &   &   & 0 [1.5mm]
& 0      &  Ddots &    &        &    &   &   & a_{n-d_u+1,n}  [1.5mm]
& Vdots & Ddots &    &        &    &   &   &   [1.5mm]
&       &  &    &        &    &   &   &  Vdots [1.5mm]
& 0  & Cdots &    & 0 & a_{n,n-d_1+1}   & Cdots  &   &  a_{nn}
end{pNiceMatrix}$

end{document}