What is the best way to indicate repeated off diagonal elements in a matrix/array?

Question

I'd like to typeset a matrix of the following kind: When the symbols involved are big, like, in place of $r$, suppose we had $\mu(k-1)$ and in place of $\lambda$, we had $\mu(k-2)$, the matrix B below becomes very ugly, especially due to the $\ddots$ looking so ugly.

Is there a nicer way to typeset a matrix like the one below.

---

I have seen that the off diagonal entries are often replaced by a big and prominent entry if they are all same. I'd be happy if someone comes up with a trick to do that as well. Probably, it is something standard and I am unaware of it.

Answer 1

This is a very common problem with matrix patterns and to be honest, I don't like that \<>dots solutions at all. I have a strong opinionated view about such use and I tend to think that they don't work at super- and sub- diagonals of the matrix.

So no matter what the solution is, one should always choose to carry the message across as opposed to complying with some ugly standard. Therefore I usually go with one of the following solutions

1. Bite the bullet and typeset the matrix properly such that the dots are unambiguous.

   \documentclass{article}
   \usepackage{amsmath}
   \begin{document}
   \[ AA^T = B = rI + 
   \begin{bmatrix}
   0       &\lambda &\ldots  &\lambda\\
   \lambda & 0      &\ddots  &\vdots\\
   \vdots  &\ddots  &0       &\lambda\\
   \lambda &\ldots  &\lambda &0
   \end{bmatrix}
   \]
   \end{document}
   

   

2. Avoid confusing drawings and define meaningful (hopefully!) shortcuts, e.g. you can define all ones matrix with blackboard 1 and subtract I from that instead of J. You don't gain a lot by replacing (1-I) by J in terms of document space.

   \documentclass{article}
   \usepackage{bbm}
   \begin{document}
   \[ AA^T = B = rI + \lambda(\mathbbm{1}-I) \]
   \end{document}
   

   

3. Draw it properly with any graphics package, TikZ, PSTricks, METAPOST etc. as given in Diagonal dots spanning multiple lines/columns of a matrix

Answer 2

Here's an idea. I sort of threw it together so manual adjustments to p{3.5ex} and \scalebox{2} will probably be necessary to get what you want. There are likely better ways to accomplish the same thing.

\documentclass{minimal}
\usepackage{array}
\usepackage{graphicx}
\usepackage{multirow}
\begin{document}

\[
\left[
\begin{array}{*{5}{>{\centering$}p{3.5ex}<{$}}}
r   &   &   &\multicolumn{2}{c}{\multirow{2}{*}{\scalebox{2}{$\lambda$}}}   \\
    &   r   &   &   &\\
    &   &\ddots &   &\\
\multicolumn{2}{c}{\multirow{2}{*}{\scalebox{2}{$\lambda$}}}&&r&\\
    &   &   &   &r
\end{array}
\right]
\]

\end{document}

Which gives the following

Answer 3

You want to convey the idea that the \mu(k-1) coefficients are repeated on the diagonal and that the other coefficients are all equal to \mu(k-2). So why don't you try the following?

\[
AA^T=B=
\begin{bmatrix}
\mu(k-1) & \mu(k-2) & \mu(k-2) & \dots & \mu(k-2) \\
\mu(k-2) & \mu(k-1) & \mu(k-2) & \dots & \mu(k-2)\\
\hdotsfor{5} \\
\mu(k-2) & \dots & \mu(k-2) & \mu(k-2) & \mu(k-1)
\end{bmatrix}
=(\mu(k-1)-\mu(k-2))I_{v}+\mu(k-2)J_{v}
\]

(which probably will need to be split into two lines)

You might want to add a supplementary line of the form

\mu(k-2) & \dots & \mu(k-2) & \mu(k-1) & \mu(k-2) \

just before the last line.

Answer 4

I suggest to use the package nicematrix which has functionalities for this problem. Tikz nodes are automatically created for each cell of the matrix and the dotted lines are drawn with Tikz.

\documentclass{article}
\usepackage{nicematrix}
\begin{document}
\renewcommand{\arraystretch}{1.5}
\[\begin{pNiceMatrix}
\mu(k-1) & \mu(k-2) & \Cdots   & \mu(k-2) \\
\mu(k-2) & \Ddots   & \Ddots   & \Vdots   \\
\Vdots   & \Ddots   &          & \mu(k-2) \\
\mu(k-2) & \Cdots   & \mu(k-2) & \mu(k-1)       
\end{pNiceMatrix}\]
\end{document}

Answer 5

Instead of using $\mu(k-1)$, you could use $\mu_{k-1}$ to save some space in each entry of your matrix.

As Peter has suggested, create a sample and let us know how you would like it changed. Then we could help you better.