我希望格式化以下等式：
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\centering
\begin{align*}
\det\left(\mathbf{A}_{\mp}\right)
&=
\det
\begin{pmatrix}
a_{2,1} \mp a_{1,1}\\
a_{2,2} \mp a_{1,2}\\
a_{2,3} \mp a_{1,3}\\
\end{pmatrix}
=
\det
\begin{pmatrix}
a_{2,1}\\
a_{2,2} \mp a_{1,2}\\
a_{2,3} \mp a_{1,3}\\
\end{pmatrix}
\mp
\det
\begin{pmatrix}
a_{1,1}\\
a_{2,2} \mp a_{1,2}\\
a_{2,3} \mp a_{1,3}\\
\end{pmatrix}\\
&=
\det
\begin{pmatrix}
a_{2,1}\\
a_{2,2}\\
a_{2,3} \mp a_{1,3}\\
\end{pmatrix}
\mp
\det
\begin{pmatrix}
a_{2,1}\\
a_{1,2}\\
a_{2,3} \mp a_{1,3}\\
\end{pmatrix}
\mp\left\{
\det
\begin{pmatrix}
a_{1,1}\\
a_{2,2}\\
a_{2,3} \mp a_{1,3}\\
\end{pmatrix}
\mp
\det
\begin{pmatrix}
a_{1,1}\\
a_{1,2}\\
a_{2,3} \mp a_{1,3}\\
\end{pmatrix}
\right\}\\
&=
\det
\begin{pmatrix}
a_{2,1}\\
a_{2,2}\\
a_{2,3}\\
\end{pmatrix}
\mp
\det\begin{pmatrix}
a_{2,1}\\
a_{2,2}\\
a_{1,3}\\
\end{pmatrix}
\mp\left[
\det
\begin{pmatrix}
a_{2,1}\\
a_{1,2}\\
a_{2,3}\\
\end{pmatrix}
\mp
\det
\begin{pmatrix}
a_{2,1}\\
a_{1,2}\\
a_{1,3}\\
\end{pmatrix} \right]\\
&\mp
\left\{
\det
\begin{pmatrix}
a_{1,1}\\
a_{2,2}\\
a_{2,3}\\
\end{pmatrix}
\mp
\det\begin{pmatrix}
a_{1,1}\\
a_{2,2}\\
a_{1,3}\\
\end{pmatrix}
\mp\left[
\det
\begin{pmatrix}
a_{1,1}\\
a_{1,2}\\
a_{2,3}\\
\end{pmatrix}
\mp
\det\begin{pmatrix}
a_{1,1}\\
a_{1,2}\\
a_{1,3}\\
\end{pmatrix}
\right]
\right\}\\
&=
\det
\begin{pmatrix}
a_{2,1}\\
a_{2,2}\\
a_{2,3}\\
\end{pmatrix}
\mp
\det\begin{pmatrix}
a_{2,1}\\
a_{2,2}\\
a_{1,3}\\
\end{pmatrix}
\mp
\det
\begin{pmatrix}
a_{2,1}\\
a_{1,2}\\
a_{2,3}\\
\end{pmatrix}
+
\det
\begin{pmatrix}
a_{2,1}\\
a_{1,2}\\
a_{1,3}\\
\end{pmatrix}\\
&\mp
\det
\begin{pmatrix}
a_{1,1}\\
a_{2,2}\\
a_{2,3}\\
\end{pmatrix}
+
\det
\begin{pmatrix}
a_{1,1}\\
a_{2,2}\\
a_{1,3}\\
\end{pmatrix}
+
\det
\begin{pmatrix}
a_{1,1}\\
a_{1,2}\\
a_{2,3}\\
\end{pmatrix}
\mp
\det
\begin{pmatrix}
a_{1,1}\\
a_{1,2}\\
a_{1,3}\\
\end{pmatrix}
\end{align*}
\end{document}
我的方法是对齐前两行和后四行的所有“det”项。我已经尝试使用嵌套alignedat环境和vphantom/来实现这一点hphantom。然而，仍然存在很多错位：
\documentclass{article}
\usepackage{amsmath}
\newcommand{\hspaceone}{\hphantom{\left\{\vphantom{\det
\begin{pmatrix}
a_{1,1}\\
a_{1,2}\\
a_{1,3}\\
\end{pmatrix}}\right.}}
\newcommand{\hspacetwo}{\hphantom{\left\{\vphantom{\det
\begin{pmatrix}
a_{1,1}\\
a_{1,2}\\
a_{1,3}\\
\end{pmatrix}}\right.}}
\newcommand{\vspaceone}{\vphantom{\det
\begin{pmatrix}
a_{1,1}\\
a_{2,2}\\
a_{2,3} \mp a_{1,3}\\
\end{pmatrix}}}
\newcommand{\vspacetwo}{\vphantom{\det
\begin{pmatrix}
a_{1,1}\\
a_{2,2} \\
a_{2,3} \mp a_{1,3}\\
\end{pmatrix}}}
\newcommand{\vspacethree}{\vphantom{\det
\begin{pmatrix}
a_{2,1}\\
a_{1,2}\\
a_{2,3}\\
\end{pmatrix}}}
\newcommand{\vspacefour}{\vphantom{\det
\begin{pmatrix}
a_{2,1}\\
a_{1,2}\\
a_{1,3}\\
\end{pmatrix}}}
\newcommand{\vspacefive}{\vphantom{\det
\begin{pmatrix}
a_{1,1}\\
a_{1,2}\\
a_{1,3}\\
\end{pmatrix}}}
\newcommand{\vspacesix}{\vphantom{\det
\begin{pmatrix}
a_{1,1}\\
a_{1,2}\\
a_{2,3}\\
\end{pmatrix}}}
\newcommand{\vspaceseven}{\vphantom{\det
\begin{pmatrix}
a_{1,1}\\
a_{1,2}\\
a_{1,3}\\
\end{pmatrix}}}
\newcommand{\vspaceeight}{\vphantom{\det
\begin{pmatrix}
a_{1,1}\\
a_{1,2}\\
a_{1,3}\\
\end{pmatrix}}}
\begin{document}
\thispagestyle{empty}
\begin{align*}
\det\left(\mathbf{A}_{\mp}\right)
&
\begin{alignedat}[t]{6}
&=\hspaceone&&
\det
\begin{pmatrix}
a_{2,1} \mp a_{1,1}\\
a_{2,2} \mp a_{1,2}\\
a_{2,3} \mp a_{1,3}\\
\end{pmatrix}
&&=&&
\det
\begin{pmatrix}
a_{2,1}\\
a_{2,2} \mp a_{1,2}\\
a_{2,3} \mp a_{1,3}\\
\end{pmatrix}
&&\mp&&
\det
\begin{pmatrix}
a_{1,1}\\
a_{2,2} \mp a_{1,2}\\
a_{2,3} \mp a_{1,3}\\
\end{pmatrix}\\
&=\hspacetwo&&
\det
\begin{pmatrix}
a_{2,1}\\
a_{2,2}\\
a_{2,3} \mp a_{1,3}\\
\end{pmatrix}
&&\mp&&
\det
\begin{pmatrix}
a_{2,1}\\
a_{1,2}\\
a_{2,3} \mp a_{1,3}\\
\end{pmatrix}
&&\mp\left\{\vspaceone\right.&&
\det
\begin{pmatrix}
a_{1,1}\\
a_{2,2}\\
a_{2,3} \mp a_{1,3}\\
\end{pmatrix}\mp
\det
\begin{pmatrix}
a_{1,1}\\
a_{1,2}\\
a_{2,3} \mp a_{1,3}\\
\end{pmatrix}
\left.\vspacetwo\right\}
\end{alignedat}\\[0.1cm]
&
\begin{alignedat}[b]{8}
&=&&
\det
\begin{pmatrix}
a_{2,1}\\
a_{2,2}\\
a_{2,3}\\
\end{pmatrix}
&&\mp&&
\det\begin{pmatrix}
a_{2,1}\\
a_{2,2}\\
a_{1,3}\\
\end{pmatrix}
&&\mp\left[\vspacethree\right.&&
\det
\begin{pmatrix}
a_{2,1}\\
a_{1,2}\\
a_{2,3}\\
\end{pmatrix}
&&\mp&&
\det
\begin{pmatrix}
a_{2,1}\\
a_{1,2}\\
a_{1,3}\\
\end{pmatrix} \left.\vspacefour\right]\\
&\mp \left\{\vspacefive\right.&&
\det
\begin{pmatrix}
a_{1,1}\\
a_{2,2}\\
a_{2,3}\\
\end{pmatrix}
&&\mp&&
\det\begin{pmatrix}
a_{1,1}\\
a_{2,2}\\
a_{1,3}\\
\end{pmatrix}
&&\mp\left[\vspacesix\right.&&
\det
\begin{pmatrix}
a_{1,1}\\
a_{1,2}\\
a_{2,3}\\
\end{pmatrix}
&&\mp&&
\det\begin{pmatrix}
a_{1,1}\\
a_{1,2}\\
a_{1,3}\\
\end{pmatrix}
\left.\vspaceseven\right]
\left.\vspaceeight\right\}\\
&=&&
\det
\begin{pmatrix}
a_{2,1}\\
a_{2,2}\\
a_{2,3}\\
\end{pmatrix}
&&\mp&&
\det\begin{pmatrix}
a_{2,1}\\
a_{2,2}\\
a_{1,3}\\
\end{pmatrix}
&&\mp&&
\det
\begin{pmatrix}
a_{2,1}\\
a_{1,2}\\
a_{2,3}\\
\end{pmatrix}
&&+&&
\det
\begin{pmatrix}
a_{2,1}\\
a_{1,2}\\
a_{1,3}\\
\end{pmatrix}\\
&\mp&&
\det
\begin{pmatrix}
a_{1,1}\\
a_{2,2}\\
a_{2,3}\\
\end{pmatrix}
&&+&&
\det
\begin{pmatrix}
a_{1,1}\\
a_{2,2}\\
a_{1,3}\\
\end{pmatrix}
&&+&&
\det
\begin{pmatrix}
a_{1,1}\\
a_{1,2}\\
a_{2,3}\\
\end{pmatrix}
&&\mp&&
\det
\begin{pmatrix}
a_{1,1}\\
a_{1,2}\\
a_{1,3}\\
\end{pmatrix}
\end{alignedat}
\end{align*}
\end{document}
我怎样才能正确地对齐这些det术语？
答案1
我会使用单一align*环境。然后，只有在正确输入数学部分后，我才会插入一些精心选择的\mskip指令来微调水平对齐。话虽如此，我认为没有必要进行微调。
\documentclass{article}
\usepackage{amsmath,mleftright}
\mleftright
\begin{document}
\begin{align*}
\det(\mathbf{A}_{\mp})
&= \mskip32mu
\det \begin{pmatrix}
a_{2,1} \mp a_{1,1}\\ a_{2,2} \mp a_{1,2}\\ a_{2,3} \mp a_{1,3}
\end{pmatrix} \\[1.5ex]
&= \mskip32mu
\det \begin{pmatrix}
a_{2,1}\\ a_{2,2} \mp a_{1,2}\\ a_{2,3} \mp a_{1,3}
\end{pmatrix}
\mp
\det \begin{pmatrix}
a_{1,1}\\ a_{2,2} \mp a_{1,2}\\ a_{2,3} \mp a_{1,3}
\end{pmatrix} \\[1.5ex]
&= \mskip32mu
\det \begin{pmatrix}
a_{2,1}\\ a_{2,2}\\ a_{2,3} \mp a_{1,3}
\end{pmatrix}
\mp
\det \begin{pmatrix}
a_{2,1}\\ a_{1,2}\\ a_{2,3} \mp a_{1,3}
\end{pmatrix} \\
&\quad
\mp
\left\{
\det \begin{pmatrix}
a_{1,1}\\ a_{2,2}\\ a_{2,3} \mp a_{1,3}
\end{pmatrix}
\mp
\det \begin{pmatrix}
a_{1,1}\\ a_{1,2}\\ a_{2,3} \mp a_{1,3}
\end{pmatrix}
\right\} \\[1.5ex]
&= \mskip32mu
\det \begin{pmatrix}
a_{2,1}\\ a_{2,2}\\ a_{2,3}
\end{pmatrix}
\mp
\det \begin{pmatrix}
a_{2,1}\\ a_{2,2}\\ a_{1,3}
\end{pmatrix}
\mp
\left[
\det \begin{pmatrix}
a_{2,1}\\ a_{1,2}\\ a_{2,3}
\end{pmatrix}
\mp
\det \begin{pmatrix}
a_{2,1}\\ a_{1,2}\\ a_{1,3}
\end{pmatrix}
\right] \\
&\quad \mp
\left\{
\det \begin{pmatrix}
a_{1,1}\\ a_{2,2}\\ a_{2,3}
\end{pmatrix}
\mp
\det \begin{pmatrix}
a_{1,1}\\ a_{2,2}\\ a_{1,3}
\end{pmatrix}
\mp
\left[
\det \begin{pmatrix}
a_{1,1}\\ a_{1,2}\\ a_{2,3}
\end{pmatrix}
\mp
\det \begin{pmatrix}
a_{1,1}\\ a_{1,2}\\ a_{1,3}
\end{pmatrix}
\right]
\right\} \\[1.5ex]
&= \mskip16mu
\det \begin{pmatrix}
a_{2,1}\\ a_{2,2}\\ a_{2,3}
\end{pmatrix}
\mp
\det \begin{pmatrix}
a_{2,1}\\ a_{2,2}\\ a_{1,3}
\end{pmatrix}
\mp
\det \begin{pmatrix}
a_{2,1}\\ a_{1,2}\\ a_{2,3}
\end{pmatrix}
+
\det \begin{pmatrix}
a_{2,1}\\ a_{1,2}\\ a_{1,3}
\end{pmatrix} \\
&\quad \mp
\det \begin{pmatrix}
a_{1,1}\\ a_{2,2}\\ a_{2,3}
\end{pmatrix}
+
\det \begin{pmatrix}
a_{1,1}\\ a_{2,2}\\ a_{1,3}
\end{pmatrix}
+
\det \begin{pmatrix}
a_{1,1}\\ a_{1,2}\\ a_{2,3}
\end{pmatrix}
\mp
\det \begin{pmatrix}
a_{1,1}\\ a_{1,2}\\ a_{1,3}
\end{pmatrix}
\end{align*}
\end{document}