# Can split and array work together?

I have the following problem. I need an equation which contains arrays and which should be on different lines because too long for one line.

This is the code:

$$\begin{split} -\frac{r_{uv}^\perp\left(r_{uv}^\perp\right)^T}{||p_v-p_u||}T(\Psi_u)^T=\\ & \frac{\left[ \begin{array}{cc} r_{uv_y}^2 & -r_{uv_x}r_{uv_y}\\ -r_{uv_x}r_{uv_y} & r_{uv_x}^2 \end{array} \right]}{||p_v-p_u||} \left[ \begin{array}{cc} \cos(\Psi_u) & \sin(\Psi_u)\\ -\sin(\Psi_u) & \cos(\Psi_u) \end{array} \right] = & \begin{array}{cc} -r_{uv_y}^2c_{\Psi_u}-r_{uv_x}r_{uv_y}s_{\Psi_u} & r_{uv_y}^2s_{\Psi_u}+r_{uv_x}r_{uv_y}c_{\Psi_u}\\ r_{uv_x}r_{uv_y}c_{\Psi_u}+r_{uv_x}^2s_{\Psi_u} & r_{uv_x}r_{uv_y}s_{\Psi_u}-r_{uv_x}^2c_{\Psi_u} \end{array} \end{split}$$


The error I get is the following:

! Extra alignment tab has been changed to \cr.
<template> }\$\hfill \endtemplate
l.753 \end{split}
You have given more \span or & marks than there were
in the preamble to the \halign or \valign now in progress.
So I'll assume that you meant to type \cr instead.


I think the error comes from the thing that for the array I need a \\ character and inside a \split envitonment it can't work.

Can you help me with this? Thanks a lot.

EDIT:

My hardcoded solution for now is the following. But I know it is not the best. I created an equation* (\begin{equation*}) which is without reference number and another one with the reference number ().

\begin{equation*}
-\frac{r_{uv}^\perp\left(r_{uv}^\perp\right)^T}{||p_v-p_u||}T(\Psi_u)^T=
\frac{\left[
\begin{array}{cc}
r_{uv_y}^2 & -r_{uv_x}r_{uv_y}\\
-r_{uv_x}r_{uv_y} & r_{uv_x}^2
\end{array}
\right]}{||p_v-p_u||}
\left[
\begin{array}{cc}
\cos(\Psi_u) & \sin(\Psi_u)\\
-\sin(\Psi_u)  &  \cos(\Psi_u)
\end{array}
\right]
=
\end{equation*}
$$\left[ \begin{array}{cc} -r_{uv_y}^2c_{\Psi_u}-r_{uv_x}r_{uv_y}s_{\Psi_u} & r_{uv_y}^2s_{\Psi_u}+r_{uv_x}r_{uv_y}c_{\Psi_u}\\ r_{uv_x}r_{uv_y}c_{\Psi_u}+r_{uv_x}^2s_{\Psi_u} & r_{uv_x}r_{uv_y}s_{\Psi_u}-r_{uv_x}^2c_{\Psi_u} \end{array} \right]$$


(You're missing several \\ (double backslash) directives, at the end of each array environment as well as between rows 2 and 3 of the multi-line equation. Once that's fixed, you'll find that split and array environments are entirely compatible with each other.)

I suggest you use bmatrix ("matrix with square brackets") environments instead of the "plain" array environments. The typeset result will be much more compact-looking, which is probably something you want.

The amsmath package provides the macro \lVert and \rVert; use them, rather than ||. In the example code below, I set up a macro called \norm that makes use of \lVert and \rVert.

\documentclass{article}
$$\begin{split} &{-}\frac{r_{uv}^\perp(r_{uv}^\perp)^T}{\norm{p_v-p_u}}\,T(\Psi_u)^T\\ &\qquad= \frac{\begin{bmatrix} r_{uv_y}^2 & -r_{uv_x}r_{uv_y}\\ -r_{uv_x}r_{uv_y} & r_{uv_x}^2 \end{bmatrix}}{\norm{p_v-p_u}} \begin{bmatrix*}[r] \cos(\Psi_u) & \sin(\Psi_u)\\ -\sin(\Psi_u) & \cos(\Psi_u)\\ \end{bmatrix*} \\ &\qquad= \begin{bmatrix} -r_{uv_y}^2c_{\Psi_u}-r_{uv_x}r_{uv_y}s_{\Psi_u} & r_{uv_y}^2s_{\Psi_u}+r_{uv_x}r_{uv_y}c_{\Psi_u}\\ r_{uv_x}r_{uv_y}c_{\Psi_u}+r_{uv_x}^2s_{\Psi_u} & r_{uv_x}r_{uv_y}s_{\Psi_u}-r_{uv_x}^2c_{\Psi_u} \end{bmatrix} \end{split}$$