bmatrix: how to align elements' subscripts?

Question

For example with the code below:

\begin{bmatrix}
\mathbf{P}^-_{k} & \mathbf{C}_k\\
\mathbf{C}_k & \mathbf{S}_k
\end{bmatrix}

you will get a result looking like this:

It is apparent that those subscripts k in the matrix are not aligned both horizontally and vertically

How to properly align those subscripts in bmatrix environment?

Or are there any other matrix environments could cope with this well?

Answer 1

To align the 4 terms on their subscripts, I suggest you combine a bmatrix*[r] environment (provided by the mathtools package) with a \mathrlap{-} instruction (also provided by the mathtools package).

Update: to perform vertical alignment of the k subscripts in the first row, I suggest you provide add a \vphantom{-} superscript term to \mathbf{C}_k term in the upper-right cell.

The result of the adjustments is shown in the lower matrix:

\documentclass{article}
\usepackage{mathtools} % for bmatrix* env. and \mathrlap macro
\begin{document}
\[
\begin{bmatrix}
\mathbf{P}^{-}_{k} & \mathbf{C}_k \\
\mathbf{C}_k       & \mathbf{S}_k
\end{bmatrix}
\]

\[
\begin{bmatrix*}[r]
\mathbf{P}^{\mathrlap{-}}_{k} & \mathbf{C}^{\vphantom{-}}_k \\
\mathbf{C}_k                  & \mathbf{S}_k
\end{bmatrix*}
\]
\end{document}

Answer 2

Here are two possibilities:

\documentclass{article}
\usepackage{amsmath}

\begin{document}
\[
  \begin{bmatrix}
    \mathbf{P}^{-}_{k} & \mathbf{C}^{\vphantom{-}}_k\\
    \mathbf{C}_k & \mathbf{S}_k
  \end{bmatrix}
  \begin{bmatrix}
    \mathbf{P}_{k}\llap{${}^{-}\mkern -3mu$} & \mathbf{C}_k\\
    \mathbf{C}_k & \mathbf{S}_k
  \end{bmatrix}
\]
\end{document}

Note: the second method uses manual adjustment for the horizontal position of the minus exponent (see the \mkern -3mu).