Vertical Alignment in Array Environment

Question

I have produced the following array

\begin{equation*}
\begin{array}{c|ccc}
\hline
{}          &  {\bf{b}}_1  &  {\bf{b}}_2   &  {\bf{b}}_3  \\
\hline
{\bf{a}}_1  &  \cos\theta  &  -\sin\theta  &  0  \\
{\bf{a}}_2  &  \sin\theta  &  \cos\theta   &  0  \\
{\bf{a}}_3  &      0       &       0       &  1  \\
\hline
\end{array}
\end{equation*}

where the output looks like

How can I vertically align the sin and cos in the second column?

Answer 1

You could insert a \phantom{-} instruction immediately before \cos\theta in the second row.

Oh, and don't use \bf -- use \mathbf instead. \bf has been deprecated in LaTeX documents since 1994. It still works with the article, report, and book document classes, but it no longer works with the KOMA-script and memoir classes.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
\begin{array}{c|ccc}
\hline
     &  \mathbf{b}_1  &  \mathbf{b}_2   &  \mathbf{b}_3  \\
\hline
\mathbf{a}_1  &  \cos\theta  &            -\sin\theta  &  0 \\
\mathbf{a}_2  &  \sin\theta  &  \phantom{-}\cos\theta  &  0 \\
\mathbf{a}_3  &      0       &                  0      &  1 \\
\hline
\end{array}
\end{equation*}
\end{document}

---

Addendum: To make the array more "beautiful" -- a criterion you've mentioned in a follow-up comment :-) -- you may want to both fine-tune the horizontal positioning of the second and third data columns and give the entire array a more "open" look, e.g., by using the line-drawing macros of the booktabs package.

\documentclass{article}
\usepackage{amsmath,booktabs}
\begin{document}
\begin{equation*}
\begin{array}{@{}ccc@{\qquad}c@{}}
\toprule
& \mathbf{b}_1 & \phantom{-}\mathbf{b}_2 & \mathbf{b}_3 \\
\cmidrule(l){2-4}
\mathbf{a}_1  &  \cos\theta  &            -\sin\theta & 0 \\
\mathbf{a}_2  &  \sin\theta  &  \phantom{-}\cos\theta & 0 \\
\mathbf{a}_3  &      0       &  \phantom{-}0          & 1 \\
\bottomrule
\end{array}
\end{equation*}
\end{document}

Answer 2

Another option in this case is to use an r column alignment for the data and \multicolumn{1}{c}{} to center the headings and zero:

Code:

\documentclass{article}
\usepackage{amsmath}

\newcommand*{\Mc}[1]{\multicolumn{1}{c}{#1}}%

\begin{document}
\begin{equation*}
\begin{array}{c|rrc}
\hline
     &  \Mc{\mathbf{b}_1}  &  \Mc{\mathbf{b}_2}   &  \Mc{\mathbf{b}_3}  \\
\hline
\mathbf{a}_1  &  \cos\theta  & -\sin\theta  &  0 \\
\mathbf{a}_2  &  \sin\theta  &  \cos\theta  &  0 \\
\mathbf{a}_3  &    \Mc{0}     &    \Mc{0}   &  1 \\
\hline
\end{array}
\end{equation*}
\end{document}