Question: ```
\documentclass{article}
\usepackage{amsmath}
\usepackage{array}
\usepackage{mathtools}
\begin{document}
\renewcommand{\arraystretch}{1.2}
\newcommand{\minus}{\scalebox{0.4}[1.0]{$-$}}
\[
\begin{bmatrix*}[r]
  0&  \minus\frac{1}{2} &\frac{1}{2} \\
  \minus\frac{1}{2}&  0&\minus\frac{1}{2}\\
  \frac{1}{2}&  \minus\frac{1}{2}&0
\end{bmatrix*}
\]
\end{document}

```

[![enter image description here](https://i.stack.imgur.com/1yvlc.png)](https://i.stack.imgur.com/1yvlc.png)

How to reduce the number “0” size to fit fraction "1/2"? (reduce height of "0" ?)

---

update sample

As below photo shows the proportion close to 1/3

[![enter image description here](https://i.stack.imgur.com/Ofr0I.jpg)](https://i.stack.imgur.com/Ofr0I.jpg)

Answer: 
I wouldn't reduce the size of the `0` numerals. If you believe that they look too big in relation to the text-style `\frac{1}{2}` expressions, maybe what's *really* needed is to replace the `\frac` terms with their decimal representations -- of course while aligning the numbers on their (explicit or implicit decimal markers.

[![enter image description here](https://i.stack.imgur.com/K0r1B.png)](https://i.stack.imgur.com/K0r1B.png)

```none
\documentclass{article}
\usepackage{mathtools}  % for 'bmatrix*' env.
\usepackage{siunitx}    % for 'S' column type
\begin{document}
\[
\renewcommand\arraystretch{1.33}
\begin{bmatrix*}[r]
   0           & -\frac{1}{2} &  \frac{1}{2} \\
  -\frac{1}{2} &  0           & -\frac{1}{2} \\
   \frac{1}{2} & -\frac{1}{2} &  0
\end{bmatrix*}
\]

\[
\left[ % note: no need to increase the value of '\arraystretch'
\begin{array}{@{} *{3}{S[table-format=-1.1]} @{}}
   0   & -0.5 &  0.5 \\
  -0.5 &  0   & -0.5\\
   0.5 & -0.5 &  0
\end{array} 
\right]
\]
\end{document}

```
I would say that your sample actually suggests the opposite: "I want to preserve regular size even for numerators and denominators". Use `\dfrac` instead of `\frac`.

Also, why do you have special treatment for minus? Why the `-` isn't enough?

```
\documentclass{article}

\usepackage{amsmath}
\usepackage{array}
\usepackage{mathtools}

\begin{document}
\renewcommand{\arraystretch}{2}
\[
  \begin{bmatrix*}[r]
    0             &  -\dfrac{1}{2} & \dfrac{1}{2}  \\
    -\dfrac{1}{2} &  0             & -\dfrac{1}{2} \\
    \dfrac{1}{2}  &  -\dfrac{1}{2} & 0
  \end{bmatrix*}
\]
\end{document}

```

[![enter image description here](https://i.stack.imgur.com/QLU1E.png)](https://i.stack.imgur.com/QLU1E.png)