Math & Science ⇒ "Advanced" matrices

[x42bn6]

Does anyone know how to do matrices but a bit more?

Of course it's a little bit hard without any code, but consider the matrix:

Code: Select all

1 2 2 2 2 2
2 1 2 2 2 2
2 2 1 2 2 2
2 2 2 1 2 2
2 2 2 2 1 2
2 2 2 2 2 1

I'd like to be able to do something like put 1s on the diagonal and then put a big "2" in the top-right and bottom-left parts of the matrix.

Anyone have any ideas?

[Stefan Kottwitz]

Hi,

that's no problem even without any package:

Code: Select all

\documentclass[a4paper,10pt]{article}
\begin{document}
\[
\left(
  \begin{array}{cccccc}
    1 & \\
      & 1 & & & \mbox{\Huge $2$}\\
      & & 1 & \\
      & & & 1 & \\
      & \mbox{\Huge $2$} & & & 1 \\
      & & & & & 1
  \end{array}
\right)
\]
\end{document}

There are packages like easybmat and blkmatrix providing support for block matrices.

Stefan

[localghost]

An alternative to Stefan's approach.

Code: Select all

\documentclass[11pt,a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{multirow}

\begin{document}
  \[
    \begin{pmatrix}
      1 & & & & \multirow{3}{*}{\Huge 2} & \\
      & 1 & & & & \\
      & & 1 & & & \\
      & \multirow{3}{*}{\Huge 2} & & 1 & & \\
      & & & & 1 & \\
      & & & & & 1
    \end{pmatrix}
  \]
\end{document}

For more information refer to the manuals of the used packages.

The »Math mode« document might give some more useful hints to handle that. Stefan already mentioned a package from the easy bundle which provides several packages for mathematical expressions.

[lalop]

Don't know of any packages. I would just make a newcommand using a counter for the number of times you've used it:

Code: Select all

\usepackage{calc}
\usepackage{ifthen}
%
\newcounter{rownumber}
\newcounter{columnnumber}

% Filldiagonal{diagonalvalue}{other value}{element counter}{row size}
%check if diagonal, puts as diagonalvalue, otherwise other value
\newcommand{\filldiagonal}[4]{%
%
% Much easier to think of the rows and columns starting at 0,
%then the modulus gives column number, integer divison gives row number
%
\setcounter{rownumber}{\value{#3}/#4}%
\setcounter{columnnumber}{\value{#3}-\value{rownumber}*#4}%
\ifthenelse{\value{columnnumber}=\value{rownumber}}{#1}{#2}%
\stepcounter{#3}%
%
}

You'd still have to copy and paste the function into every element, but at least it's easier.

Code: Select all

\newcounter{eleme}
\setcounter{eleme}{0}

\begin{array}{cccccccccc}
\filldiagonal{1}{2}{eleme}{10} & ... & \filldiagonal{1}{2}{eleme}{10}\\
\filldiagonal{1}{2}{eleme}{10}  & ... & \filldiagonal{1}{2}{eleme}{10}\\
...
\filldiagonal{1}{2}{eleme}{10} } & ... & \filldiagonal{1}{2}{eleme}{10}\\
\end{array}

And you can make similar macros for other matricies. The disadvantage is that it can take a lot of time to figure out the row, column # if you're not careful.

[lalop]

Found an even easier way, using for loops. Here's a complete document:

Code: Select all

\documentclass[11pt]{memoir}
\usepackage{ifthen}
\usepackage{forloop} 


\newcommand{\filldiagonal}[5]{
\ifthenelse{#3=#4}{#1}{#2}%
\ifthenelse{#4<#5}{ & }{\\}%
}


\begin{document}

\newcounter{rownumber}
\newcounter{columnnumber}


$$\begin{array}{cccccccccc}
\forLoop{1}{10}{rownumber}{%
	\forLoop{1}{10}{columnnumber}{%
		\filldiagonal{1}{2}{\value{rownumber}}{\value{columnnumber}}{10}%
	}%
}\end{array}$$

\end{document} 

(The artifact at the top right is just the page number.)

The weird bit, though, is that it won't let me insert the contents of the filldiagonal directly into the for loop. E.g.

Code: Select all

\documentclass[11pt]{memoir}
\usepackage{ifthen}
\usepackage{forloop} 


\newcommand{\filldiagonal}[5]{
\ifthenelse{#3=#4}{#1}{#2}%
\ifthenelse{#4<#5}{ & }{\\}%
}


\begin{document}

\newcounter{rownumber}
\newcounter{columnnumber}


$$\begin{array}{cccccccccc}
\forLoop{1}{10}{rownumber}{%
	\forLoop{1}{10}{columnnumber}{%
		\ifthenelse{\value{rownumber} = \value{columnumber}}{1}{2}%
		\ifthenelse{\value{columnnumber}<10}{\\}{&}%	
	}
}

\end{array}$$

\end{document}

Gives errors saying "You can't use \relax after the }"

[mdk31]

An alternative to Stefan's approach.

Code: Select all

\documentclass[11pt,a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{multirow}

\begin{document}
  \[
    \begin{pmatrix}
      1 & & & & \multirow{3}{*}{\Huge 2} & \\
      & 1 & & & & \\
      & & 1 & & & \\
      & \multirow{3}{*}{\Huge 2} & & 1 & & \\
      & & & & 1 & \\
      & & & & & 1
    \end{pmatrix}
  \]
\end{document}

For more information refer to the manuals of the used packages.

The »Math mode« document might give some more useful hints to handle that. Stefan already mentioned a package from the easy bundle which provides several packages for mathematical expressions.

I think the \multirow command is having problems running in my math environment.

Code: Select all

\documentclass[twoside,12pt,openright]{report}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{array}
\usepackage{multirow}
\begin{equation}
\text{adj}({\bf A}^T \! {\bf A})_{k,k}= \left|
\begin{bmatrix}
u^1_a & ... & u^m_a \\
u^1_b & ... & u^m_b \\
\lambda & ... & \lambda
\end{bmatrix}
\begin{bmatrix}
\multirow{2}{*}{\large {\bf R}_r} & u^m_a \\ 
& u^m_b \\
0^T & \lambda
\end{bmatrix} \right|
\end{equation}
\end{document}

I'm getting errors like "Missing $ inserted" or "Missing } inserted" which I think is because of the \multirow in the equation environment.

[localghost]

I think the \multirow command is having problems running in my math environment. [...] I'm getting errors like "Missing $ inserted" or "Missing } inserted" which I think is because of the \multirow in the equation environment.

You are wrong. Obviously you haven't tested my example. Otherwise you would have found out that it's working fine. The only thing that doesn't work is your way of choosing font styles for boldface in math mode.


Best regards
Thorsten

[mdk31]

Well, I'm not sure why that is because now it's telling me that I'm not in math mode so I can't use \mathbf.

Code: Select all

\begin{equation}
\text{adj}({\bf A}^T \! {\bf A})_{k,k}= \left|
\begin{bmatrix}
u^1_a & ... & u^m_a \\
u^1_b & ... & u^m_b \\
\lambda & ... & \lambda
\end{bmatrix}
\begin{bmatrix}
\multirow{2}{*}{\large \mathbf{R}_k} & u^m_a \\ 
& u^m_b \\
0^T & \lambda
\end{bmatrix} \right|
\end{equation}
\end{document}

[mdk31]

Okay, I think I see now how to get rid of the error. But I'm still having problems with the format because I know that you can't use multirow for the second matrix. I need a command that will stretch the R_k across the second column in the first row.

Code: Select all

\documentclass[twoside,12pt,openright]{report} 
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{array}
\usepackage{multirow}
\setlength{\extrarowheight}{0.4cm}
\newcommand{\vectornorm}[1]{\left|\left|\mathbf{#1}\right|\right|}
\newcommand{\mb}[1]{\mathbf{#1}}
\begin{document}
\begin{equation}
\text{adj}(\mb{A}^T \! \mb{A})_{k,k}= \left|
\begin{bmatrix}
\multirow{2}{*}{$\mb{R}_k$} & u^m_a \\ 
& u^m_b \\
0^T & \lambda
\end{bmatrix}
\begin{bmatrix}
\multirow{2}{*}{$\mb{R}^T_k$} &  & 0 \\
u^m_a & u^m_b & \lambda \\
\end{bmatrix}\right|
\end{equation}
\end{document}