How do I create a bordered Hessian matrix in LaTeX?

Question

I am supposed to use the following matrix in a math problem:

But based on my experience with LaTeX's tables and matrices, I know this is beyond me.

Can anyone tell me how to make the following matrix? Any help would be great. I assume I need to use bmatrix but after that I am stumped.

Answer 1

Here is how I would do it:

\documentclass{article}

\usepackage{mathtools}
\usepackage{bm}

\DeclareMathOperator{\Hess}{Hess}
\newcommand*\vect[1]{\mathbf{#1}}

% http://tex.stackexchange.com/a/59955/15874
% The following piece of code measures the length of math expressions
% in order to get the length of the two horizontal rules (based on
% the chosen width of the whitespaces) in the matrix.
\makeatletter
\newcommand*\settowidthofalign[2]{%
  \setbox\z@=\vbox{
    \begin{align*}
    #2
    \ifmeasuring@\else\global\let\got@maxcolwd\maxcolumn@widths\fi
    \end{align*}
  }%
  \begingroup
  \def\or{+}\edef\x{\endgroup#1=\dimexpr\got@maxcolwd\relax}\x}
\makeatother

\newlength{\mylenA}
\newlength{\mylenB}

% Calculate length of rules.
\if \mylenA < \mylenB
  \newcommand*\ruleLength{\the\dimexpr(\mylenA-\mylenB-4*(\WhiteSpace))/2\relax}
 \else
  \newcommand*\ruleLength{\the\dimexpr(\mylenB-\mylenA-4*(\WhiteSpace))/2\relax}
\fi

% Matrix construction.
\newcommand*\Matrix[4]{%
  \left[
    \begin{array}{@{} c | c @{}}
      #1
      & \begin{array}{c}
          \vert\\
          #2\\
          \vline
          \vspace{0.5ex}
         \end{array}\\
      \hline
      \vspace{0.5ex}
      \raisebox{-0.3ex}{%
        $\rule[0.5ex]{\ruleLength}{0.4pt}
         \hspace{\WhiteSpace} #3 \hspace{\WhiteSpace}
         \rule[0.5ex]{\ruleLength}{0.4pt}$%
      }
      & \raisebox{-0.3ex}{$#4$}
    \end{array}
  \right]%
}

% Matrix entries.
\newcommand*\entryA{\Hess(f)(\vect{a}) - \lambda\Hess(g)(\vect{a})}
\newcommand*\entryB{\bm{\nabla} g(\vect{a})}
\newcommand*\entryC{D g(\vect{a})}
\newcommand*\entryD{0}

\begin{document}

% Widths of expressions in matrix entries.
\settowidthofalign{\mylenA}{\entryA}
\settowidthofalign{\mylenB}{\entryB}

\begin{equation*}
  % Width of whitespace on each side of horizontal lines.
  \def\WhiteSpace{12pt}
  % Math expression.
  H_{f,g} \binom{\vect{a}}{\lambda}
  = \Matrix{\entryA}{\entryB}{\entryC}{\entryD}
\end{equation*}

\end{document}

This might be overkill in this particular case but you now have a working construction that can be re-used for other matrices. All you have to do is

• define the entries of the new matrix (e.g., \entryE),
• define the new lengths to be used (using \newlength),
• let TeX calculate the widths of the math expressions (using \settowidthofalign),
• typeset the whole shebang (using \Matrix).

Note: I wouldn't make the \nabla bold; I think it disturbes the reading more than it helps.

Answer 2

Here is an approach with an array and some \rule commands for the extra lines inside of cells. Note that the array actually consists of four rows.

Code

\documentclass[varwidth]{standalone}
\usepackage{amsmath,bm}
\DeclareMathOperator\Hess{Hess}
\begin{document}
\begin{equation*}
\renewcommand*\a{\mathbf{a}}
\newcommand*\vl{\rule[-.3em]{.4pt}{1em}}
\newcommand*\hl{\rule[.5ex]{2em}{.4pt}}
%
H_{f,g}\binom{\a}{\lambda} = \left[\begin{array}{c|c}
                                  & \vl          \\
 \Hess(f)(\a)-\lambda\Hess(g)(\a) & \nabla g(\a) \\
                                  & \vl          \\ \hline
 \hl\quad Dg(\a) \quad\hl         & 0
\end{array}\right]
\end{equation*}
\end{document}

Output

Answer 3

Something like that?

\documentclass{article}
\usepackage{amssymb}
\usepackage{mathtools, array}
\DeclareMathOperator{\hess}{Hess}

\def\longline{\relbar\mkern-6mu\relbar}

\begin{document}

\[\setlength\extrarowheight{1pt}
  \begin{bmatrix}
    \begin{array}{c@{\,}c@{\,}c|c}
    & & & \vrule \\
    \multicolumn{3}{c|}{\hess_{f, g}(f)(\mathbf a)} & \nabla g(\mathbf a)\\
      & & & \vrule \\[-2.6ex] & & & \\
    \hline
    \longline & Dg(\mathbf a) &\longline & 0
    \end{array}
  \end{bmatrix} \]%

\end{document} 

Answer 4

How to do this using normal TeX tools:

\def\vec#1{{\bf#1}}
\def\lrule{\leaders\hrule height3pt depth-2.6pt\hskip2em \relax}
\def\Hess{\mathop{\rm Hess}\nolimits}
$$
  H_{f,g} {\vec a \choose \lambda} =
  \left[
  \vcenter{\offinterlineskip
     \halign{\hfil$#$\ \hfil\vrule height10pt depth5pt&\hfil\ $#$\hfil\cr
        & | \cr
        \Hess(f)(\vec a) - \lambda \Hess(g)(\vec a) & \nabla g(\vec a) \cr
        & | \cr
        \noalign{\hrule}
        \lrule\ Dg(\vec a)\ \lrule & 0 \cr
  }}
  \right]
$$