How to create new counter of equation

This can be done using a newenvironment and the amsmath to help with the tagging

I have defined the matriz environment in terms of the equation environment, and tagged it with a new counter; you can use \label and \eqref as usual.

\documentclass{article}
\usepackage{amsmath}

\newcounter{matriz}
\newenvironment{matriz}{\refstepcounter{matriz}\equation}{\tag{M\thematriz}\endequation}
\begin{document}

\begin{equation}
 y = x
\end{equation}

\begin{equation}
 y = \frac{1}{x}
\end{equation}

The of next matriz equation is 1. \eqref{test}
\begin{matriz}\label{test}
y = \sqrt x
\end{matriz}

\end{document}

amsmath with more than equation

I'd go a broader approach …

The following codes uses the environment m and its mandatory argument to use any amsmath environment (that introduces displayed math-mode) in combination with the matrix counter.

The etoolbox helps to redefine the macros \print@eqnum and \incr@eqnum. An alternative is given in the commented part of the code.

Without cmhughes’ solution the actual equation environment still uses \print@eqnum with \theequation but \incr@eqnum with matrix.

Code

\documentclass[a4paper,10pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{etoolbox}

\newcounter{matrix}
\renewcommand*{\thematrix}{M\arabic{matrix}}

\makeatletter
\def\@equationname{equation}
\newenvironment{m}[1]{%
    \def\mymathenvironmenttouse{#1}%
    \ifx\mymathenvironmenttouse\@equationname%
        \refstepcounter{matrix}%
    \else
        \patchcmd{\@arrayparboxrestore}{equation}{matrix}{}{}%          doesn't change output?
        \patchcmd{\print@eqnum}{equation}{matrix}{}{}%
        \patchcmd{\incr@eqnum}{equation}{matrix}{}{}%
%       \def\print@eqnum{\tagform@\thematrix}%                          instead of etoolbox' \pathcmd
%       \def\incr@eqnum{\refstepcounter{matrix}\let\incr@eqnum\@empty}% instead of etoolbox' \pathcmd
    \fi
    \csname\mymathenvironmenttouse\endcsname%
}{%
    \ifx\mymathenvironmenttouse\@equationname%
        \tag{\thematrix}%
    \fi
    \csname end\mymathenvironmenttouse\endcsname%
}
\makeatother
\begin{document}

\begin{equation}
 y = x
\end{equation}

\begin{equation}
 y = \frac{1}{x}
\end{equation}

The of next matriz equation is \ref{eq:M1}.
\begin{m}{equation}
 y = \sqrt x \label{eq:M1}
\end{m}

\begin{equation}
 y = \frac{1}{x}
\end{equation}

\begin{m}{align}
 y & = \sqrt x \\
 z & = y^2
\end{m}

\begin{m}{alignat}{3}
 y & = \sqrt x & \quad\text{col2l} & = \text{col2r} & \quad\text{col3l} & = \text{col3r} \\
 z & = y^2 & & & &
\end{m}

\begin{m}{equation}
 y = \sqrt x
\end{m}
\end{document}

Output

Sans-amsmath solution (without eqnarray)

Code

\documentclass[a4paper,10pt]{article}
\usepackage[utf8]{inputenc}

\newcounter{matrix}
\renewcommand*{\thematrix}{M\arabic{matrix}}

\makeatletter
\newenvironment{matriz}{%
    \def\@eqnnum{{\normalfont \normalcolor (\thematrix)}}%
    \def\equation{$$\refstepcounter{matrix}}%
    \equation%
}{%
    \endequation%
}
\makeatother

\begin{document}

\begin{equation}
 y = x
\end{equation}

\begin{equation}
 y = \frac{1}{x}
\end{equation}

The of next matriz equation is \ref{eq:m1}.

\begin{matriz}\label{eq:m1}
y = \sqrt x
\end{matriz}

\begin{equation}
 y = x
\end{equation}

\begin{matriz}
y = \sqrt x
\end{matriz}
\end{document}

Output