Please help me with the anti-circulant square matrix notation. It looks like the vector notation but has a double line arrow. \xRightarrow from mathtools wouldn't work because the arrow is in the middle of the line.

Please help me with the anti-circulant square matrix notation. It looks like the vector notation but has a double line arrow. \xRightarrow from mathtools wouldn't work because the arrow is in the middle of the line.

Here are several ways to make double arrows over symbols.

\documentclass{article}
\usepackage{amssymb}
\usepackage{accents}
\makeatletter
\def\Rightarrowfill{$\m@th\mathord= \mkern-6mu
\cleaders\hbox{$\mkern-2mu\mathord= \mkern-2mu$}\hfill
\mkern-6mu \mathord\Rightarrow$}
\def\Overrightarrow#1{\vbox{\m@th\ialign{##\crcr
\Rightarrowfill\crcr\noalign{\kern.4pt\nointerlineskip}
$\hfil\displaystyle{#1}\hfil$\crcr}}}
\makeatother
\newcommand{\vect}[1]{\accentset{\Rightarrow}{#1}}
\newcommand{\vectt}[1]{\accentset{\Longrightarrow}{#1}}
\begin{document}
Here is the usual \texttt{vec} command and my suggested \texttt{vect} for
comparison.
\[ \vec{v}\in\mathbb{Z}^{N\times N} \qquad \vect{v}\in\mathbb{Z}^{N\times N}\]
One way to deal with a wide argument is just to put the accent on the $C$.
\[ \vect{C}_\mathit{Mi}\in\mathbb{Z}^{N\times N}\]
Another way is to define \texttt{vectt} with \texttt{Longrightarrow}.
\[ \vectt{C_{\mathit{Mi}}}\in\mathbb{Z}^{N\times N}\]
A third way is to create a new stretchy macro like \texttt{overrightarrow}.
\[ \overrightarrow{C_\mathit{Mi}}\in\mathbb{Z}^{N\times N} \qquad
\Overrightarrow{C_\mathit{Mi}}\in\mathbb{Z}^{N\times N}\]
\end{document}
Note that \mathit{Mi} looks slightly better than {Mi} in the subcript.
Original solution
\documentclass{article}
\usepackage{amssymb}
\usepackage{accents}
\newcommand{\vect}[1]{\accentset{\Rightarrow}{#1}}
\begin{document}
\[ \vec{v}\in\mathbb{Z}^{N\times N}\]
\[ \vect{v}\in\mathbb{Z}^{N\times N}\]
\end{document}

Maybe a stack? The use of \useanchorwidth in the true condition means that the size of the overset does not affect the underlying math spacing.
\documentclass{article}
\usepackage{stackengine,amsfonts}
\stackMath
\def\useanchorwidth{T}
\begin{document}
\[
\stackon[1pt]{v}{\,\scriptscriptstyle\Rightarrow} \in \mathbb{Z}^{N\times N}
\]
\end{document}

vwhen we see compilable code, starting with\documentclass{...}and ending with\end{document}. – Thruston Mar 27 '15 at 11:59\xRightarrowit not meant to be used as a vector margin, but rather as a\Rightarrowwith comment. I've never seen vectors (or what ever it is) written with a double stemmed arrow. Do you have any examples from literature or articles from e.g. arxiv which uses this notation? – daleif Mar 27 '15 at 12:02