[Tex/LaTex] Split long expression inside bmatrix environment

matrices

I am new to this and so please excuse my ignorance.

I have an equation Ax = b, where A is a 3 x 3 matrix. Because some of the elements in the matrix A contain long expressions, latex is not able to fit the equation neatly across the page (it causes the equation number to overspill, see image below). I wish to avoid splitting the matrix A over two rows. Instead, I would like to split the (long) elements over two lines if possible such that the equation fits on one row across the page. Any help would be greatly appreciated. My code is as follows:

\documentclass[11pt]{book}
\usepackage{amsmath,amsfonts,amssymb,amsthm, bm}

\begin{document}

\begin{equation}
\begin{bmatrix}
\mathbf{i}_{w}\\ 
\mathbf{j}_{w}\\ 
\mathbf{k}_{w}
\end{bmatrix} = \begin{bmatrix}
\cos\gamma \cos\chi & \cos\gamma \sin\chi & -\sin\chi \\ 
\sin\mu \sin\gamma \cos\chi - \cos\mu \sin\chi & \sin\mu \sin\gamma \sin\chi + \cos\mu \cos\chi & \sin\mu \cos\gamma \\ 
\cos\mu \sin\gamma \cos\chi + \sin\mu \sin\chi & \cos\mu\sin\gamma\sin\chi-\sin\mu\cos\chi & \cos\mu\cos\gamma
\end{bmatrix}  \begin{bmatrix}
\mathbf{i}_{h}\\ 
\mathbf{j}_{h}\\ 
\mathbf{k}_{h}
\end{bmatrix}
\end{equation}

\end{document}

Best Answer

You can nest matrix, giving some more room between the main rows.

\documentclass[11pt]{book}
\usepackage{amsmath,amssymb,amsthm, bm}

\begin{document}

\begin{equation}
\begin{bmatrix}
\mathbf{i}_{w}\\ 
\mathbf{j}_{w}\\ 
\mathbf{k}_{w}
\end{bmatrix} = \begin{bmatrix}
\cos\gamma \cos\chi & \cos\gamma \sin\chi & -\sin\chi \\[1ex]
\begin{matrix}
  \sin\mu \sin\gamma \cos\chi \\
  \hfill{}- \cos\mu \sin\chi
\end{matrix}
 & 
\begin{matrix}
  \sin\mu \sin\gamma \sin\chi \\
  \hfill{}+ \cos\mu \cos\chi
\end{matrix}
 & \sin\mu \cos\gamma \\[2.5ex]
\begin{matrix}
  \cos\mu \sin\gamma \cos\chi \\
  \hfill{}+ \sin\mu \sin\chi
\end{matrix}
 &
\begin{matrix}
  \cos\mu\sin\gamma\sin\chi \\
  \hfill{}- \sin\mu\cos\chi
\end{matrix}
 & \cos\mu\cos\gamma
\end{bmatrix}  \begin{bmatrix}
\mathbf{i}_{h}\\ 
\mathbf{j}_{h}\\ 
\mathbf{k}_{h}
\end{bmatrix}
\end{equation}

\end{document}

You can also align the columns, by replicating the contents with phantoms:

\documentclass[11pt]{book}
\usepackage{amsmath,amssymb,amsthm, bm}

\begin{document}

\begin{equation}
\begin{bmatrix}
\mathbf{i}_{w}\\[1ex]
\mathbf{j}_{w}
\vphantom{\begin{matrix}
  \sin\mu \sin\gamma \cos\chi \\
  \hfill{}- \cos\mu \sin\chi
  \end{matrix}
}
\\[2.5ex]
\mathbf{k}_{w}
\vphantom{\begin{matrix}
  \cos\mu \sin\gamma \cos\chi \\
  \hfill{}+ \sin\mu \sin\chi
  \end{matrix}
}
\end{bmatrix} = \begin{bmatrix}
\cos\gamma \cos\chi & \cos\gamma \sin\chi & -\sin\chi \\[1ex]
\begin{matrix}
  \sin\mu \sin\gamma \cos\chi \\
  \hfill{}- \cos\mu \sin\chi
\end{matrix}
 & 
\begin{matrix}
  \sin\mu \sin\gamma \sin\chi \\
  \hfill{}+ \cos\mu \cos\chi
\end{matrix}
 & \sin\mu \cos\gamma \\[2.5ex]
\begin{matrix}
  \cos\mu \sin\gamma \cos\chi \\
  \hfill{}+ \sin\mu \sin\chi
\end{matrix}
 &
\begin{matrix}
  \cos\mu\sin\gamma\sin\chi \\
  \hfill{}- \sin\mu\cos\chi
\end{matrix}
 & \cos\mu\cos\gamma
\end{bmatrix}  \begin{bmatrix}
\mathbf{i}_{h}\\[1ex]
\mathbf{j}_{h}
\vphantom{\begin{matrix}
  \sin\mu \sin\gamma \cos\chi \\
  \hfill{}- \cos\mu \sin\chi
  \end{matrix}
}
\\[2.5ex]
\mathbf{k}_{h}
\vphantom{\begin{matrix}
  \cos\mu \sin\gamma \cos\chi \\
  \hfill{}+ \sin\mu \sin\chi
  \end{matrix}
}
\end{bmatrix}
\end{equation}

\end{document}

Now judge yourself about the aesthetics.

Related Solutions

[Tex/LaTex] Split a \bmatrix in two line

What about using a smallmatrix?

enter image description here

Code:

\documentclass[a4paper,twoside,12pt]{book}
\usepackage[utf8]{inputenc}
\usepackage{amsmath,bm}
\begin{document}
\[
\bm{\mu^*} =
[\begin{smallmatrix}
 17.0716 & 21.3746 & 31.2462 & 34.2847 & 37.0049 & 43.2856 & 50.8193 & 59.7093
\end{smallmatrix}]
\]
\end{document}

[Tex/LaTex] split a multiline bmatrix

I wouldn't push down the left-hand side, so I provide both renderings.

\documentclass[11pt]{book}
\usepackage{amsmath,amsfonts,amssymb,amsthm, bm}

\begin{document}

\begin{equation}\label{theta}
\begin{bmatrix}
x\\
y
\end{bmatrix} =
\!\begin{aligned}
&
\left[\begin{matrix}
  L_{1} + \delta r_{3v} + r_{3v} + \Delta r_{3}^{\circ})\cos(\theta_{1}+ \delta\theta_{1})\\
  L_{1} + \delta r_{3v} + r_{3v} + \Delta r_{3}^{\circ})\sin(\theta_{1}+ \delta\theta_{1})
\end{matrix}\right.\\
&\qquad\qquad
\left.\begin{matrix}
  {}+(\delta r_{2v} + r_{2v} + \Delta r_{3}^{\circ})\sin(\theta_{1} + \delta\theta_{1})\\
  {}-(\delta r_{2v} + r_{2v} + \Delta r_{3}^{\circ})\cos(\theta_{1} + \delta\theta_{1})
\end{matrix}\right]
\end{aligned}
\end{equation}

\begin{equation}\label{theta-alt}
\begin{aligned}
\begin{bmatrix}
x\\
y
\end{bmatrix} &=
\left[\begin{matrix}
  L_{1} + \delta r_{3v} + r_{3v} + \Delta r_{3}^{\circ})\cos(\theta_{1}+ \delta\theta_{1})\\
  L_{1} + \delta r_{3v} + r_{3v} + \Delta r_{3}^{\circ})\sin(\theta_{1}+ \delta\theta_{1})
\end{matrix}\right.\\
&\qquad\qquad
\left.\begin{matrix}
  {}+(\delta r_{2v} + r_{2v} + \Delta r_{3}^{\circ})\sin(\theta_{1} + \delta\theta_{1})\\
  {}-(\delta r_{2v} + r_{2v} + \Delta r_{3}^{\circ})\cos(\theta_{1} + \delta\theta_{1})
\end{matrix}\right]
\end{aligned}
\end{equation}

\end{document}

Note that I removed the superfluous \left( and \right). Note also the additional {} groups for making the plus and minus into binary operation symbols.

I would consider leaving the plus and minus in the top lines, so to make clear that the formula has not ended yet.

Best Answer

Related Solutions

[Tex/LaTex] Split a \bmatrix in two line

[Tex/LaTex] split a multiline bmatrix

Related Question