在 bmatrix 内对齐大元素

Question

我有一个大矩阵

\begin{align}
    \begin{bmatrix} 
    \bigg(m\Gamma_1(\kappa_1^1)\omega_1\mathbf{h}_0\mathbf{P}_1^\varepsilon + m\Gamma_2(\kappa_1^1)\sin\bigg(\frac{2\omega_1\bar\zeta x_3}{\varepsilon}\bigg)\omega_1\mathbf{h}_1\mathbf{P}^\varepsilon_1 \\
    + m\Gamma_2(\kappa_1^1)\cos\bigg(\frac{2\omega_1\bar\zeta x_3}{\varepsilon}\bigg)\omega_1\mathbf{h}_2\mathbf{P}_1^\varepsilon\bigg) & \mathbf{0} & \dots & \mathbf{0} \\
    \mathbf{0} & \ddots & \ddots & \vdots \\
    \vdots & \ddots & \ddots & \mathbf{0} \\
    \mathbf{0} & \dots & \mathbf{0} & X
    \end{bmatrix}
\end{align}

我想插入的地方

\begin{align}
    &\bigg(m\Gamma_1(\kappa_1^M)\omega_M\mathbf{h}_0\mathbf{P}_1^\varepsilon + m\Gamma_2(\kappa_1^M)\sin\bigg(\frac{2\omega_M\bar\zeta x_3}{\varepsilon}\bigg)\omega_M\mathbf{h}_1\mathbf{P}^\varepsilon_M \\
    &+ m\Gamma_2(\kappa_1^1)\cos\bigg(\frac{2\omega_M\bar\zeta x_3}{\varepsilon}\bigg)\omega_M\mathbf{h}_2\mathbf{P}_M^\varepsilon\bigg)
\end{align}

“X” 位于哪里。实现此目的的最佳程序是什么？>?>?

Answer 1

我会放置两个都环境的左上角和右下角元素bmatrix位于不同的行上。

我还将使用内联分数符号来表示三角项，从而节省大量垂直空间。

\documentclass{article}
\usepackage{mathtools}

\begin{document}
\begin{align*}
\mathbf{A} &=
    \begin{bmatrix} \,
      \mathbf{U} & \mathbf{0} & \dots      & \mathbf{0} \\
      \mathbf{0} & \ddots     & \ddots     & \vdots     \\
      \vdots     & \ddots     & \ddots     & \mathbf{0} \\
      \mathbf{0} & \dots      & \mathbf{0} & \mathbf{V}
    \end{bmatrix} \\
\shortintertext{where}
\mathbf{U}
  &= m\Gamma_1(\kappa_1^1)\omega_1\mathbf{h}_0\mathbf{P}_1^\varepsilon 
   + m\Gamma_2(\kappa_1^1)\sin(2\omega_1\bar\zeta x_3/\varepsilon)\omega_1\mathbf{h}_1\mathbf{P}^\varepsilon_1 \\
  &\quad + m\Gamma_2(\kappa_1^1)\cos(2\omega_1\bar\zeta x_3/\varepsilon) \omega_1\mathbf{h}_2\mathbf{P}_1^\varepsilon \\
\shortintertext{and}
\mathbf{V}
  &= m\Gamma_1(\kappa_1^M)\omega_M\mathbf{h}_0\mathbf{P}_1^\varepsilon + m\Gamma_2(\kappa_1^M)\sin(2\omega_M\bar\zeta x_3/\varepsilon)\omega_M\mathbf{h}_1\mathbf{P}^\varepsilon_M \\
  &\quad+ m\Gamma_2(\kappa_1^1)\cos(2\omega_M\bar\zeta x_3/\varepsilon) \omega_M\mathbf{h}_2\mathbf{P}_M^\varepsilon
\end{align*}
\end{document}

---

附录：原帖作者在评论中指出，大矩阵是块对角矩阵。结合此信息，我们可以更简洁地重新表述该内容，如下

\documentclass{article}
\usepackage{mathtools} % for '\shortintertext' macro
\DeclareMathOperator{\diag}{diag}
\begin{document}
\begin{align*}
\mathbf{A} &= \diag(\mathbf{U}_1,\dots,\mathbf{U}_M)\,,
\shortintertext{where}
\mathbf{U}_j
  &= \,\phantom{+} m\Gamma_1(\kappa_1^j)\omega_j\mathbf{h}_0\mathbf{P}_j^\varepsilon \\
  &\phantom{{}=} + m\Gamma_2(\kappa_1^j)\sin(2\omega_j\bar\zeta x_3/\varepsilon)\omega_j\mathbf{h}_1\mathbf{P}_j^\varepsilon \\
  &\phantom{{}=} + m\Gamma_2(\kappa_1^j)\cos(2\omega_j\bar\zeta x_3/\varepsilon) \omega_j\mathbf{h}_2\mathbf{P}_j^\varepsilon 
\end{align*}
for $j=1,\dots,M$.
\end{document}