Problem related with aligned

I'm trying to place 3 equations with some dots between them and I don't know why only the first \cdots is right aligned and the others are a mess. This is the code:

\begin{equation}
\begin{aligned}
(\mathcal{H}_{11}- &S_{11}E_i)c_{1i}+(\mathcal{H}_{12}- &S_{12}E_i)c_{2i}+ &\cdots+(\mathcal{H}_{1n}- &S_{1n}E_i)c_{ni}=0\\
(\mathcal{H}_{21}- &S_{21}E_i)c_{1i}+(\mathcal{H}_{22}- &S_{22}E_i)c_{2i}+ &\cdots+(\mathcal{H}_{2n}- &S_{2n}E_i)c_{ni}=0\\
&\cdots&\cdots&\cdots&\cdots\\
(\mathcal{H}_{n1}- &S_{n1}E_i)c_{ni}+(\mathcal{H}_{n2}- &S_{n2}E_i)c_{2i}+ &\cdots+(\mathcal{H}_{nn}- &S_{nn}E_i)c_{ni}=0\\
\label{eq:secular}
\end{aligned}
\end{equation}

Thank you very much

Edit: Thanks everyone for the help, maybe an image about what i'm trying to obtain would be better than words: • You have to think on it like this: You need a & for each alignment point, and a & between each set of alignments (left and right pairs around an alignment &), so you need to figure out which &'s does what. It is not clear to me which parts should be aligned in your example. – daleif Apr 8 '16 at 11:49

(Edited to provide a few more \vdots instructions, per the OP's updated request)

Instead of using an aligned environment, I would use a basic array environment to align the various parts of the equation. This way, it's straightforward to align all + and = symbols as well as the remaining constituent parts of the system of equations. Observe also the four \vdots instructions in the third row. \documentclass{article}
\usepackage{array}
\begin{document}
\begin{equation} \label{eq:secular}
\setlength\arraycolsep{0pt}
\renewcommand\arraystretch{1.25}
\begin{array}{*{4}{c >{{}}c<{{}}} c}
(\mathcal{H}_{11}- S_{11}E_i)c_{1i} & + &
(\mathcal{H}_{12}- S_{12}E_i)c_{2i} & + &
\cdots & + &
(\mathcal{H}_{1n}- S_{1n}E_i)c_{ni} & = & 0\\
(\mathcal{H}_{21}- S_{21}E_i)c_{1i} & + &
(\mathcal{H}_{22}- S_{22}E_i)c_{2i} & + &
\cdots & + &
(\mathcal{H}_{2n}- S_{2n}E_i)c_{ni}& = & 0\\
\vdots & & \vdots & & \vdots & & \vdots & &  \\
(\mathcal{H}_{n1}- S_{n1}E_i)c_{ni}& + &
(\mathcal{H}_{n2}- S_{n2}E_i)c_{2i}& + &
\cdots& + &
(\mathcal{H}_{nn}- S_{nn}E_i)c_{ni}& = & 0 \\
\end{array}
\end{equation}
\end{document}

You can do it with alignedat with a couple of tricks.

1. I locally define \2 to provide a double index as wide as nn so the alignment will be automatic between the variables; the \2 macro will only be available in that equation environment.

2. I use the low level instruction \multispan to insert a row of dots.

Full code

\documentclass{article}
\usepackage{amsmath,calc}

\begin{document}

\begin{equation}
\label{eq:secular}
\newcommand{\2}{%
_{\makebox[\widthof{$nn$}][l]{$#1$}}%
}
\begin{alignedat}{4}
(\mathcal{H}\2{11}- S\2{11}E_i)c\2{1i}
&+(\mathcal{H}\2{12}-S\2{12}E_i)c\2{2i}
&&+\dotsb
&&+(\mathcal{H}\2{1n}-S\2{1n}E_i)c\2{ni}
&&=0\\
(\mathcal{H}\2{21}-S\2{21}E_i)c\2{1i}
&+(\mathcal{H}\2{22}-S\2{22}E_i)c\2{2i}
&&+\dotsb
&&+(\mathcal{H}\2{2n}-S\2{2n}E_i)c\2{ni}
&&=0\\
\multispan{8}{\dotfill}\\[1ex]
%&\dotsb&\dotsb&\dotsb&\dotsb\\
(\mathcal{H}\2{n1}-S\2{n1}E_i)c\2{ni}
&+(\mathcal{H}\2{n2}-S\2{n2}E_i)c\2{2i}
&&+\dotsb
&&+(\mathcal{H}\2{nn}-S\2{nn}E_i)c\2{ni}
&&=0
\end{alignedat}
\end{equation}

\end{document} You also can do that with the alignedat environment. I propose two codes: the first aligns the + and = signs, and the first , the second aligns all signs, at the cost of some slightly distorted space:

\documentclass[a4paper, 11pt]{book}
\usepackage[utf8]{inputenc}
\usepackage{fourier, erewhon}

\usepackage{mathtools}

\begin{document}

\begin{equation}
\begin{alignedat}{4}
(\mathcal{H}_{11}&-S_{11}E_i)c_{1i} & & +(\mathcal{H}_{12} -S_{12}E_i)c_{2i} & + \cdots & +(\mathcal{H}_{1n} - S_{1n}E_i)c_{ni} & =0\\
(\mathcal{H}_{21}&-S_{21}E_i)c_{1i} & & +(\mathcal{H}_{22}-S_{22}E_i)c_{2i} & + \cdots & +(\mathcal{H}_{2n}- S_{2n}E_i)c_{ni} & =0\\
% &\cdots&\cdots&\cdots&\cdots\\
(\mathcal{H}_{n1}&-S_{n1}E_i)c_{ni} & & +(\mathcal{H}_{n2}-S_{n2}E_i)c_{2i} & +\cdots & +(\mathcal{H}_{nn} - S_{nn}E_i)c_{ni} &= 0
\label{eq:secular}
\end{alignedat}
\end{equation}

\begin{equation}
\begin{alignedat}{6}
(\mathcal{H}_{11} & -S_{11}E_i)c_{1i} & & {} +(\mathcal{H}_{12} & & {}-S_{12}E_i)c_{2i} &{} + \cdots & +(\mathcal{H}_{1n} && {} - S_{1n}E_i)c_{ni} & =0\\
(\mathcal{H}_{21} & -S_{21}E_i)c_{1i} & & {} +(\mathcal{H}_{22}& & {}-S_{22}E_i)c_{2i} &{} + \cdots & +(\mathcal{H}_{2n} && {} - S_{2n}E_i)c_{ni} & =0\\
% &\cdots&\cdots&\cdots&\cdots\\
(\mathcal{H}_{n1} & -S_{n1}E_i)c_{ni} & & {} +(\mathcal{H}_{n2}& & {}-S_{n2}E_i)c_{2i} &{} + \cdots & +(\mathcal{H}_{nn} && {} - S_{nn}E_i)c_{ni} &= 0
\label{eq:secular}
\end{alignedat}
\end{equation}

\end{document} • You have two unnecessary trailing \\. – Manuel Apr 9 '16 at 19:35
• Oh! yes. They come from the O.P.'s post. Thanks for pointing it. – Bernard Apr 9 '16 at 19:50