# How to input the staggered array?

How to input the staggered array as the expression like this:

The expressions are in hexagonal fashion. Are there packages for this situation?

thank you.

Here, I use TABstacks to make the data stacks, and the \scaleleftright[max-width]{left}{content}{right} to add the brackets. Note that in the second matrix, I actually use a small negative "tabbedgap" of -1pt (i.e., column sep) to overlap the columns slightly. By comparison, I use a +1pt gap in the first matrix

\documentclass{article}
\usepackage{scalerel,tabstackengine,amssymb,amsmath}
\stackMath
\begin{document}
$\setstacktabbedgap{1pt} A_h = \scaleleftright[1.5ex]{\langle}{\tabbedCenterstack{ &0&&0&\\ 0&&0&&0\\ &0&&0& }}{\rangle} \text{, and } \setstacktabbedgap{-1pt} B_h =\scaleleftright[1.5ex]{\langle}{\tabbedCenterstack{ &-1&&-1&\\ -1&&6+\varepsilon^2&&-1\\ &-1&&-1& }}{\rangle}$
\end{document}


While not shown here, uniform column width can be enforced by issuing \fixTABwidth{T} prior to the stacks. In so doing, a change in the tabbedgap is correspondingly called for.

If one really hates typing double &&, then this \active alternative allows the use of # to mean &&, producing the same result:

\documentclass{article}
\usepackage{scalerel,tabstackengine,amssymb,amsmath}
\stackMath
\begin{document}
$\catcode#=\active \def#{&&} \setstacktabbedgap{1pt} A_h = \scaleleftright[1.5ex]{\langle}{\tabbedCenterstack{ &0#0&\\ 0#0#0\\ &0#0& }}{\rangle} \text{, and } \setstacktabbedgap{-1pt} B_h =\scaleleftright[1.5ex]{\langle}{\tabbedCenterstack{ &-1#-1&\\ -1#6+\varepsilon^2#-1\\ &-1#-1& }}{\rangle}$
\end{document}


Three lines are covered by the standard \left< and \right> symbols.

Here's an hexagon environment that can receive an optional argument for setting the width of the cells (default 1em):

\documentclass{article}
\usepackage{amsmath,collcell}

\newcolumntype{h}{>{\collectcell\hd}c<{\endcollectcell}}
\newcolumntype{k}[1]{@{\hspace{-#1\hexawidth}}}
\newcommand{\hd}[1]{\makebox[\hexawidth]{$#1$}}
\newlength{\hexawidth}

\newenvironment{hexagon}[1][1em]
{\setlength{\hexawidth}{#1}
\left<
\begin{array}{k{.33333}*{4}{hk{.5}}hk{.33333}}}
{\end{array}\right>}

\begin{document}
$A_{h}= \begin{hexagon} & 0 && 0 \\ 0 && 0 && 0 \\ & 0 && 0 \\ \end{hexagon} \qquad B_{h}= \begin{hexagon}[4em] & -1 && -1 \\ -1 && 6+\varepsilon^2 && -1 \\ & -1 && -1 \\ \end{hexagon}$
\end{document}


Note that the \\ in the last row is necessary because of how collcell works.

I didn't know scalerel and \scaleleftright command, so I've copied from Steven's answer. Thanks.

But I knew array which can be also used for these expressions.

\documentclass{article}
\usepackage{scalerel,amsmath,array}
\usepackage{lmodern}

\begin{document}
$A_h = \scaleleftright[1.5ex]{\langle}{\begin{array}{@{}c@{}c@{}c@{}c@{}c@{}c@{}} & 0 & & 0 & \\ 0 & & 0 & & 0 \\ & 0 & & 0 &\\ \end{array}}{\rangle}, \text{and}\ B_h = \scaleleftright[1.5ex]{\langle}{\begin{array}{@{}c@{}c@{}c@{}c@{}c@{}c@{}} & -1 & & -1 & \\ -1 & & 6+\epsilon^2 & & -1 \\ & -1 & & -1 &\\ \end{array}}{\rangle}$
\end{document}
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