A way to left align the matrix and then place text on the right side

Question

I've a 2x2 matrix, that I want to left align inside the flalign Environment, I also want to place the three sentences below inside the environment on the right side. However I dont find a solution how to do it, because of the matrix notation.

\documentclass[a4paper, abstracton, bibtotocnumbered,liststotoc,12pt]{scrartcl}

\usepackage[T1]{fontenc}
\usepackage[latin1]{inputenc} %% für Windows
\usepackage[ngerman]{babel}

\usepackage{amsthm}
\usepackage{mathtools}

\begin{document}
Die Kovarianzmatrix $\Sigma=\frac{1}{N}X'X$ kann in vier Teile partitioniert werden
\begin{flalign*}
&\Sigma=
  \begin{bmatrix}
    \Sigma_{1,1} & \Sigma_{1,2}  \\
    \Sigma_{2,1} & \Sigma_{2,2}  \\
  \end{bmatrix}
\end{flalign*}
$\Sigma_{1,1}$: Kovarianzen der relevanten Regressoren.
$\Sigma_{2,2}$: Kovarianzen der irrelevanten Regressoren.
$\Sigma_{1,2}$: Kovarianzen der relevanten mit den irrelevanten Regressoren. 
\end{document}

Answer 1

Here is a solution with a tabular:

\documentclass[a4paper, abstracton, bibtotocnumbered, liststotoc,12pt]{scrartcl}

\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc} %% für Windows
\usepackage[ngerman]{babel}

\usepackage{amsthm}
\usepackage{mathtools}

\begin{document}

sein muss. Die Kovarianzmatrix $\Sigma=\frac{1}{N}X'X$ kann in vier Teile partitioniert werden
\begin{flalign*}
&\Sigma=
  \begin{bmatrix}
    \Sigma_{1,1} & \Sigma_{1,2} \\
    \Sigma_{2,1} & \Sigma_{2,2} \\
  \end{bmatrix} & & & & \begin{tabular}{>{$}l<{$}@{\ }
>{\footnotesize}l@{}}
\Sigma_{1,1}: & Kovarianzen der relevanten Regressoren. \\
\Sigma_{2,2}: & Kovarianzen der irrelevanten Regressoren. \\
\Sigma_{1,1}: & Kovarianzen der relevanten mit den irrelevanten\\
 & Regressoren.
\end{tabular}
\end{flalign*}

\end{document} 

Answer 2

There are numerous possibilities to achieve something like this, here is one.

\documentclass[a4paper, abstracton, bibtotocnumbered,liststotoc,12pt]{scrartcl}

\usepackage[T1]{fontenc}
\usepackage[latin1]{inputenc} %% für Windows
\usepackage[ngerman]{babel}

\usepackage{amsthm}
\usepackage{mathtools}
\usepackage{tabularx,multirow}
\begin{document}
\noindent
sein muss. Die Kovarianzmatrix $\Sigma=\frac{1}{N}X'X$ kann in vier Teile
partitioniert werden\\
\begin{tabularx}{\textwidth}{p{3.5cm}X}
\multirow{3}{3.5cm}{$\displaystyle
\Sigma=
  \begin{bmatrix}
    \Sigma_{1,1} & \Sigma_{1,2}  \\
    \Sigma_{2,1} & \Sigma_{2,2}  \\
  \end{bmatrix} 
$} &
$\Sigma_{1,1}$: Kovarianzen der relevanten Regressoren.\\
&
$\Sigma_{2,2}$: Kovarianzen der irrelevanten Regressoren.\\
&
$\Sigma_{1,1}$: Kovarianzen der relevanten mit den irrelevanten Regressoren. \\
\end{tabularx}
\end{document}

Whether or not I personally would use something like this is a different question.