# Toeplitz matrix in LaTeX

How do I create a Toeplitz matrix like the following in LaTeX?

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Thanks a lot my friend – tanha Apr 29 '14 at 8:10

\documentclass{article}
\usepackage{mathtools}
\begin{document}

$%\arraycolsep=4pt G = \begin{bmatrix*}[r] 1 \\ 2&1\\ -1&2&1\\ &-1&2&1\\ &&-1&2&1\\ &&&-1&2&1\\ &&&&&&\ddots\\ &&&&&&&\ddots\\ &&&&&&&&\ddots\\ &&&&&&&&&1 \end{bmatrix*}$
\end{document}


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I think the last row must contain all non-zero elements: -1 2 1 – Robert Fuster Apr 28 '14 at 9:00
Thanks a lot my friend – tanha Apr 29 '14 at 8:10

Here you go:

\documentclass{article}
\pagestyle{empty}% for cropping
\usepackage{amsmath}
\begin{document}
\begin{equation*}
G =
\begin{bmatrix}
1 \cr
2&1\cr
-1&2&1\cr
&-1&2&1\cr
&&-1&2&1\cr
&&&-1&2&1\cr
&&&&&&\ddots\cr
&&&&&&&\ddots\cr
&&&&&&&&\ddots\cr
&&&&&&&&&1\cr
\end{bmatrix}
\end{equation*}
\end{document}


To get nicer alignment of the minus-signs you could use an array with right-aligned columns

\documentclass{article}
\pagestyle{empty}% for cropping
\usepackage{amsmath}
\begin{document}
\begin{equation*}
G =
\left[
\begin{array}{*{10}r}
1 \cr
2&1\cr
-1&2&1\cr
&-1&2&1\cr
&&-1&2&1\cr
&&&-1&2&1\cr
&&&&&&\ddots\cr
&&&&&&&\ddots\cr
&&&&&&&&\ddots\cr
&&&&&&&&&1\cr
\end{array}
\right]
\end{equation*}
\end{document}


-
to get the right alignment, it's simpler to load the mathtools package and write: begin{bmatrix*}[r] … \end{bmatrix*}. – Bernard Apr 28 '14 at 8:36
Is there a reason to use \cr instead of \? – Manuel Apr 28 '14 at 14:53
@Manuel Because I often use plain TeX and there is no \\. In this case both are equivalent. Also \cr is primitive, hence it doesn't need to get expanded, you may save half a nano-second by that. – Henri Menke Apr 28 '14 at 15:06
Thanks a lot my friend – tanha Apr 29 '14 at 8:10

Although late to the race my entry is presented below:

\documentclass[12pt]{article}
\usepackage{mathtools}
\usepackage{amssymb}

\begin {document}
$$\begin{pmatrix} 2 & -1 & 0 & \cdots & \cdots & \cdots & \cdots & 0\\ -1 & 2 & -1 & 0 & & & & \vdots\\ 0 & -1 & 2 & -1 & \ddots & & & \vdots\\ \vdots & 0 & \ddots & \ddots & \ddots & \ddots & & \vdots\\ \vdots & & \ddots & \ddots & \ddots & \ddots & 0 & \vdots\\ \vdots & & & \ddots & -1 & 2 & -1 & 0\\ \vdots & & & & 0 & -1 & 2 & -1\\ 0 & \cdots & \cdots & \cdots & \cdots & 0 & -1 & 2\\ \end{pmatrix}$$
\end{document}


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@Mico Sure, here is a reference ece.umn.edu/~mihailo/software/lqrsp/mass_spring.html – sunspots Feb 21 '15 at 23:47
The matrix G is also referred to as a band matrix. – sunspots Feb 21 '15 at 23:48
Your proposed solution produces a symmetric matrix, whereas the OP appears to want to produce an asymmetric matrix with all elements above the diagonal equal to zero. – Mico Feb 22 '15 at 1:22
@Mico My entry is final. – sunspots Feb 22 '15 at 1:56
You can do whatever you want. An answer is usually considered to be more helpful, though, if it addresses the actual question that's been posed, rather than some other problem. – Mico Feb 22 '15 at 3:05