4

This is what I generated for a set of equivalent definitions of positive semi-definiteness.

\documentclass[10pt]{article}

% for fancy math
\usepackage{amsmath}

% rank operator
\DeclareMathOperator*{\rank}{rank}

% Matrix transpose
\newcommand{\trans}[1]{\ensuremath{{#1}^\top}}

% for extra space at the end of abbreviation
\usepackage{xspace}

% positive semi-definite
\newcommand{\psd}{\textsc{psd}\xspace}

% boldface uppercase letters for matrices
\newcommand{\Abf}{\ensuremath{\mathbf A}}
\newcommand{\Bbf}{\ensuremath{\mathbf B}}

% boldface lowercase letters for vectors
\newcommand{\xbf}{\ensuremath{\mathbf x}}

% for math blackboard font
\usepackage{amssymb}
% set of real numbers
\newcommand{\Rbb}{\ensuremath{\mathbb R}}

\usepackage{palatino}
\usepackage[sc]{mathpazo}

\begin{document}
\noindent
For any real symmetric matrcies $\Abf$ such that $\rank(\Abf_{n\times n})=r$,
the following statements are equivalent
and any one of them can serve as the definition of
\emph{positive semi-definite} (\psd) matrices.
\begin{itemize}
  \item $\trans\xbf \Abf\xbf \geq 0$ for any non-zero vector
    $\xbf\in\Rbb^{n\times 1}$.
    \hfill\refstepcounter{equation}\textup{(\theequation)}%
  \item All the $n$ eigenvalues of $\Abf$ are non-negative.
    \hfill\refstepcounter{equation}\textup{(\theequation)}%
  \item $\Abf=\trans\Bbf \Bbf$ for some $\Bbf$ with $\rank(\Bbf)=r$.
    \hfill\refstepcounter{equation}\textup{(\theequation)}%
\end{itemize}

\end{document}

enter image description here

As these definitions are all equivalent, I'd like to number them as (1a), (1b), and (1c) instead of (1), (2), (3). I'm not sure whether I can use subequations environment as I want to keep three different definitions as a text in an itemized list.

Any suggestions?

user19906
  • 1,415

3 Answers3

4

Just add:

\begin{subequations}
...
\end{subequations}

around your itemize environment.

nickie
  • 4,378
3

Here is an alternative view on such a layout, which avoids inserting the equation number manually:

enter image description here

\documentclass[10pt]{article}

% for fancy math
\usepackage{amsmath}

% rank operator
\DeclareMathOperator*{\rank}{rank}

% Matrix transpose
\newcommand{\trans}[1]{\ensuremath{{#1}^\top}}

% for extra space at the end of abbreviation
\usepackage{xspace}

% positive semi-definite
\newcommand{\psd}{\textsc{psd}\xspace}

% boldface uppercase letters for matrices
\newcommand{\Abf}{\ensuremath{\mathbf A}}
\newcommand{\Bbf}{\ensuremath{\mathbf B}}

% boldface lowercase letters for vectors
\newcommand{\xbf}{\ensuremath{\mathbf x}}

% for math blackboard font
\usepackage{amssymb}
% set of real numbers
\newcommand{\Rbb}{\ensuremath{\mathbb R}}

\usepackage{palatino}
\usepackage[sc]{mathpazo}

\newcommand{\mathitem}{\hspace*{1.2em}&\bullet\hspace*{\labelsep}}
\begin{document}
\noindent
For any real symmetric matrcies $\Abf$ such that $\rank(\Abf_{n\times n})=r$,
the following statements are equivalent
and any one of them can serve as the definition of
\emph{positive semi-definite} (\psd) matrices.
\begin{itemize}
  \item $\trans\xbf \Abf\xbf \geq 0$ for any non-zero vector
    $\xbf\in\Rbb^{n\times 1}$.
    \hfill\refstepcounter{equation}\textup{(\theequation)}%
  \item All the $n$ eigenvalues of $\Abf$ are non-negative.
    \hfill\refstepcounter{equation}\textup{(\theequation)}%
  \item $\Abf=\trans\Bbf \Bbf$ for some $\Bbf$ with $\rank(\Bbf)=r$.
    \hfill\refstepcounter{equation}\textup{(\theequation)}%
\end{itemize}

\noindent
For any real symmetric matrcies $\Abf$ such that $\rank(\Abf_{n\times n})=r$,
the following statements are equivalent
and any one of them can serve as the definition of
\emph{positive semi-definite} (\psd) matrices.
\begin{subequations}
\makeatletter\@fleqntrue\makeatother
\begin{align}
  \mathitem \text{$\trans\xbf \Abf\xbf \geq 0$ for any non-zero vector
    $\xbf\in\Rbb^{n\times 1}$.} \\
  \mathitem \text{All the $n$ eigenvalues of $\Abf$ are non-negative.} \\
  \mathitem \text{$\Abf=\trans\Bbf \Bbf$ for some $\Bbf$ with $\rank(\Bbf)=r$.}
\end{align}
\end{subequations}

\end{document}

The idea is to set a regular align in a subequations environment, momentarily flushing it to the left margin (through an activation of \@fleqntrue). If you which to increase the gap between the elements (since they're slightly more tight under align), use \\[<len>] where you specify <len>.

Moriambar
  • 11,466
Werner
  • 603,163
2

Why not just make your list:

\begin{itemize}
  \item $\trans\xbf \Abf\xbf \geq 0$ for any non-zero vector
    $\xbf\in\Rbb^{n\times 1}$.
    \hfill\refstepcounter{equation}\textup{(\theequation a)}%
  \item All the $n$ eigenvalues of $\Abf$ are non-negative.
    \hfill\refstepcounter{equation}\textup{(\theequation b)}%
  \item $\Abf=\trans\Bbf \Bbf$ for some $\Bbf$ with $\rank(\Bbf)=r$.
    \hfill\refstepcounter{equation}\textup{(\theequation c)}%
\end{itemize}
codeAndStuff
  • 488