How do I create a Toeplitz matrix like the following in LaTeX?
4 Answers
\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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1I think the last row must contain all non-zero elements:
-1 2 1Robert Fuster– Robert Fuster2014-04-28 09:00:36 +00:00Commented Apr 28, 2014 at 9:00
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}
-
3to get the right alignment, it's simpler to load the
mathtoolspackage and write:begin{bmatrix*}[r] … \end{bmatrix*}.Bernard– Bernard2014-04-28 08:36:08 +00:00Commented Apr 28, 2014 at 8:36 -
Is there a reason to use
\crinstead of `\`?Manuel– Manuel2014-04-28 14:53:42 +00:00Commented Apr 28, 2014 at 14:53 -
1@Manuel Because I often use plain TeX and there is no
\\. In this case both are equivalent. Also\cris primitive, hence it doesn't need to get expanded, you may save half a nano-second by that.Henri Menke– Henri Menke2014-04-28 15:06:58 +00:00Commented Apr 28, 2014 at 15:06
Although late to the race my entry is presented below:
\documentclass[12pt]{article}
\usepackage{mathtools}
\usepackage{amssymb}
\begin {document}
\begin{equation}
\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{equation}
\end{document}
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@Mico Sure, here is a reference ece.umn.edu/~mihailo/software/lqrsp/mass_spring.htmlsunspots– sunspots2015-02-21 23:47:09 +00:00Commented Feb 21, 2015 at 23:47
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The matrix G is also referred to as a band matrix.sunspots– sunspots2015-02-21 23:48:12 +00:00Commented Feb 21, 2015 at 23:48
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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– Mico2015-02-22 01:22:21 +00:00Commented Feb 22, 2015 at 1:22
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@Mico My entry is final.sunspots– sunspots2015-02-22 01:56:43 +00:00Commented Feb 22, 2015 at 1:56
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1You 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– Mico2015-02-22 03:05:08 +00:00Commented Feb 22, 2015 at 3:05
With {bNiceMatrix} of nicematrix. You need several compilations.
\documentclass{article}
\usepackage{nicematrix}
\begin{document}
\[\renewcommand{\arraystretch}{1.3}
\setlength{\arraycolsep}{4pt}
\begin{bNiceMatrix}[columns-width=auto,xdots/shorten=6pt]
1 \\
2 & 1 \\
-1 & 2 & 1 \\
& -1 & 2 & 1 \\
& & -1 & 2 & 1 \\
& & & \Ddots[shorten-end=0pt] & \Ddots & \Ddots[draw-first] \\
\\
\\
& & & & & & -1 & 2 & 1 \\
\end{bNiceMatrix}
\]
\end{document}
