[Tex/LaTex] How to write the Hessian

math-modesymbols

Do you know if there is any command to write "Hess f"? What is the standard? Should I just write it as text?

Thank you!

Best Answer

The following will work nicely:

\documentclass{article}

\usepackage{amsmath}
\usepackage{mathtools}
\DeclareMathOperator{\Hessian}{Hess}

\begin{document}
\begin{align}
  (\Hessian f)_{ij} &\equiv \frac{\partial^{2} f}{\partial x_{i} \partial x_{j} } \\
  \Hessian\left( \frac{x^{2}}{y} \right) &= 
  \begin{bmatrix}
    \frac{2}{y} & - \frac{2x}{y^{2}} \\
    -\frac{2x}{y^{2}} & \frac{2x^{2}}{y^{3}}
  \end{bmatrix}
\end{align}
\end{document}

Related Solutions

[Tex/LaTex] How to write Stirling numbers of the second kind

The following is taken from amsmath and uses \genfrac - a generic fraction function:

enter image description here

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\DeclareRobustCommand{\stirling}{\genfrac\{\}{0pt}{}}
\begin{document}
% Source: http://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind
In mathematics, particularly in combinatorics, a Stirling number of the second kind 
is the number of ways to partition a set of $n$~objects into $k$~non-empty subsets and 
is denoted by~$S(n,k)$ or~$\stirling{a}{b}$. Stirling numbers of the second kind occur 
in the field of mathematics called combinatorics and the study of partitions.
\end{document}

How does this work? \genfrac takes five arguments to create a structure (from the amsmath documentation; section 4.11.3 The \genfrac command, p 14):

The last two correspond to \frac’s numerator and denominator; the first two are optional delimiters [...]; the third is a line thickness override [0 implies an invisible rule]; and the fourth argument is a mathstyle override: integer values 0-3 select respectively \displaystyle, \textstyle, \scriptstyle, and \scriptscriptstyle. If the third argument is left empty, the line thickness defaults to ‘normal’.

So \genfrac\{\}{0pt}{} creates a fraction with an invisible horizontal rule (third argument is 0pt), left and right delimiter given by \{ and \}, respectively and no specific math style (an empty {} fourth argument). \stirling doesn't include a fifth and sixth argument for \genfrac (numerator and denominator), because this is implicitly supplied by the user as the two "arguments" to \stirling.

In a similar manner (perhaps for reference), amsmath defines

\newcommand{\frac}[2]{\genfrac{}{}{}{}{#1}{#2}}
\newcommand{\tfrac}[2]{\genfrac{}{}{}{1}{#1}{#2}}
\newcommand{\binom}[2]{\genfrac{(}{)}{0pt}{}{#1}{#2}}

using \genfrac.

[Tex/LaTex] How to write “ℰ”

Here are 3 more script fonts for which there exists a LaTeX package (in math mode): Dutchcal(from the esstix 13 font), Boondox (from the stix fonts) (two variants) and Adobe's Bickham. All exist in regular and boldface. The following code allows to test them, commenting and uncommenting the relevant lines:

        \documentclass[12pt]{article}
        \usepackage[utf8]{inputenc}

        \usepackage{dutchcal}
        %\usepackage{boondox-cal}
        %\usepackage{boondox-calo}
        %\usepackage{bickham}

        \pagestyle{empty}

        \begin{document}%
        \textbf{Dutchcal: }
        %\textbf{boondox-cal}
        %\textbf{boondox-calo}
        %\textbf{bickham}
        $ \begin{array}[t]{c@{\quad}c}
            \verb+ \mathcal + & \verb+ \mathbcal + \\[6pt]
            \mathcal{E} & \mathbcal{E}
            \end{array} $

        \end{document}

enter image description here

Best Answer

Related Solutions

[Tex/LaTex] How to write Stirling numbers of the second kind

[Tex/LaTex] How to write “ℰ”

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