如何在 LaTeX 中编写雅可比矩阵

Question

我正在使用 LaTeX 编写这个雅可比矩阵：

\mathbf{u_{i,j}}=\left[\begin{array}{ccc}
\frac{\partial u_1}{\partial x_1} & \frac{\partial u_1}{\partial x_2} & \frac{\partial u_1}{\partial x_3} \\
\frac{\partial u_2}{\partial x_1} & \frac{\partial u_2}{\partial x_2} & \frac{\partial u_2}{\partial x_3 \\
\frac{\partial u_3}{\partial x_1} & \frac{\partial u_3}{\partial x_2} & \frac{\partial u_3}{\partial x_3
\end{array}\right],

但它没有被编译。

我该如何写这个？

Answer 1

@Sebastiano回答显示了您需要做什么才能使代码编译时不出现错误或警告消息。为了使矩阵更易于阅读和更具视觉吸引力，您可能还需要 (a) 增加行之间的空白量和 (b) 使用环境bmatrix（由包提供amsmath）代替基本array环境来更紧凑地排版矩阵 - 具体来说，方括号和矩阵本身之间的空间更小。

\documentclass{article}
\usepackage{amsmath} % for 'bmatrix' environment
\begin{document}
\[
\mathbf{u}_{i,j} =
\begin{bmatrix}
  \frac{\partial u_1}{\partial x_1} & 
    \frac{\partial u_1}{\partial x_2} & 
    \frac{\partial u_1}{\partial x_3} \\[1ex] % <-- 1ex more space between rows of matrix
  \frac{\partial u_2}{\partial x_1} & 
    \frac{\partial u_2}{\partial x_2} & 
    \frac{\partial u_2}{\partial x_3} \\[1ex]
  \frac{\partial u_3}{\partial x_1} & 
    \frac{\partial u_3}{\partial x_2} & 
    \frac{\partial u_3}{\partial x_3}
\end{bmatrix}
\]
\end{document}

Answer 2

如同米科的答案...

但是，为了缩短代码编写时间，请使用以下physics包：

\documentclass{article}
\usepackage{amsmath} % for 'bmatrix' environment
\usepackage{physics} % for 'pdv' macro

\begin{document}
\[\renewcommand\arraystretch{1.6}
\mathbf{u}_{i,j} =
\begin{bmatrix}
  \pdv{u_1}{x_1} &
    \pdv{u_1}{x_2} &
    \pdv{u_1}{x_3} \\%[1ex] % <-- 1ex more space between rows of matrix
  \pdv{u_2}{x_1} &
    \pdv{u_2}{x_2} &
    \pdv{u_2}{x_3} \\%[1ex]
  \pdv{u_3}{x_1} &
    \pdv{u_3}{x_2} &
    \pdv{u_3}{x_3}
\end{bmatrix}
\]
\end{document}

Answer 3

首先，您有两个语法错误，即，}在 之后缺少两个 (右花括号) \partial x_3。其次，array环境必须置于数学模式。

\documentclass[a4paper]{article}
\usepackage{amsmath}
\begin{document}

\[
\mathbf{u_{i,j}}=\left[\begin{array}{ccc}
\frac{\partial u_1}{\partial x_1} & \frac{\partial u_1}{\partial x_2} & \frac{\partial u_1}{\partial x_3} \\
    \frac{\partial u_2}{\partial x_1} & \frac{\partial u_2}{\partial x_2} & \frac{\partial u_2}{\partial x_3} \\
    \frac{\partial u_3}{\partial x_1} & \frac{\partial u_3}{\partial x_2} & \frac{\partial u_3}{\partial x_3}
\end{array}\right]
\]
\end{document}