splitting equation with matrices into multiple lines

Question

I'm struggling to split an equation with matrix math into multiple lines. I've tried multline and aligned environments with no luck. It doesn't seem to handle having the matrices within this equation.

here's my code without any splitting attempts:

\begin{equation}
    T'_{corr}(z)= 
    \begin{bmatrix} 
        n t_{0,c} + m t_{sel,c} & n t_{0,i} + m t_{sel,i} & n t_{0,j} + m t_{sel,j} & n t_{0,k} + m t_{sel,k} & n t_{0,u} + m t_{sel,u} &  n t_{0,v} + m t_{sel,v}\\        
    \end{bmatrix} 
    \begin{bmatrix} 
        \delta\phi'_c(z) \\ \delta\phi'_i(z) \\ \delta \phi'_j(z) \\ \delta\phi'_k(z)  \\ \delta\phi'_u(z) \\\delta\phi'_v(z) \\
    \end{bmatrix}
\end{equation}

Answer 1

Instead of typesetting a 6-element row vector, I would typeset the transpose of the corresponding column vector.

You're of course free to choose a different symbol than ^{T} to denote transposition.

\documentclass{article}
\usepackage{mathtools} % for '\smashoperator' macro

\begin{document}
\begin{equation}
    T'_{\mathrm{corr}}(z)= 
    \begin{bmatrix} 
        n t_{0,c} + m t_{\mathrm{sel},c} \\ 
        n t_{0,i} + m t_{\mathrm{sel},i} \\ 
        n t_{0,j} + m t_{\mathrm{sel},j} \\ 
        n t_{0,k} + m t_{\mathrm{sel},k} \\ 
        n t_{0,u} + m t_{\mathrm{sel},u} \\ 
        n t_{0,v} + m t_{\mathrm{sel},v}      
    \end{bmatrix}^{T}\!
    \begin{bmatrix} 
        \delta\phi'_c(z) \\ 
        \delta\phi'_i(z) \\ 
        \delta\phi'_j(z) \\ 
        \delta\phi'_k(z) \\ 
        \delta\phi'_u(z) \\
        \delta\phi'_v(z)
    \end{bmatrix}
    = \!\! \smashoperator[r]{\sum_{\kappa\in\{c,i,j,k,u,v\}}} 
    (nt_{0,\kappa}+mt_{\mathrm{sel},\kappa})\,\delta\phi'_{\kappa}(z)
\end{equation}
\end{document}

Answer 2

First matrix is far longer than \textwidth ... so ti may be solution to split it in three lines:

\documentclass{article}
\usepackage{mathtools}

\begin{document}
    \begin{gather}
T'_{corr}(z)=
\left[\begin{multlined}
    nt_{0,c}+ mt_{sel,c}\quad  nt_{0,i}+ mt_{sel,i} \\
    nt_{0,j}+ mt_{sel,j}\quad  nt_{0,k}+ mt_{sel,k} \\ 
    nt_{0,u}+ mt_{sel,u}\quad  nt_{0,v}+ mt_{sel,v}
\end{multlined}\right]
\begin{bmatrix}
    \delta\phi'_c(z)    \\ 
    \delta\phi'_i(z)    \\ 
    \delta \phi'_j(z)   \\ 
    \delta\phi'_k(z)    \\ 
    \delta\phi'_u(z)    \\
    \delta\phi'_v(z)
\end{bmatrix}
    \end{gather}
\end{document}