Editing Block matrix (section)

==Example==
The matrix

:<math>\mathbf{P} = \begin{bmatrix}
  1 & 2 & 2 & 7 \\
  1 & 5 & 6 & 2 \\
  3 & 3 & 4 & 5 \\
  3 & 3 & 6 & 7
\end{bmatrix}</math>

can be visualized as divided into four blocks, as 

:<math>\mathbf{P} = \left[
\begin{array}{cc|cc}
  1 & 2 & 2 & 7 \\
  1 & 5 & 6 & 2 \\
\hline
  3 & 3 & 4 & 5 \\
  3 & 3 & 6 & 7
\end{array}
\right]</math>.

The horizontal and vertical lines have no special mathematical meaning,<ref name=":3" /><ref name=":4">{{Cite book |last=Johnston |first=Nathaniel |title=Advanced linear and matrix algebra |date=2021 |publisher=Springer Nature |isbn=978-3-030-52814-0 |location=Cham, Switzerland |pages=298}}</ref> but are a common way to visualize a partition.<ref name=":3" /><ref name=":4" /> By this partition, <math>P</math> is partitioned into four 2×2 blocks, as

:<math>
  \mathbf{P}_{11} = \begin{bmatrix}
    1 & 2 \\
    1 & 5
  \end{bmatrix},\quad
  \mathbf{P}_{12} = \begin{bmatrix}
    2 & 7\\
    6 & 2
  \end{bmatrix},\quad
  \mathbf{P}_{21} = \begin{bmatrix}
    3 & 3 \\
    3 & 3
  \end{bmatrix},\quad
  \mathbf{P}_{22} = \begin{bmatrix}
    4 & 5 \\
    6 & 7
  \end{bmatrix}.
</math>

The partitioned matrix can then be written as

:<math>\mathbf{P} = \begin{bmatrix}
  \mathbf{P}_{11} & \mathbf{P}_{12} \\
  \mathbf{P}_{21} & \mathbf{P}_{22}
\end{bmatrix}.</math><ref>{{Cite book |last=Jeffrey |first=Alan |url=https://www.worldcat.org/title/639165077 |title=Matrix operations for engineers and scientists: an essential guide in linear algebra |date=2010 |publisher=Springer |isbn=978-90-481-9273-1 |location=Dordrecht [Netherlands] ; New York |pages=54 |oclc=639165077}}</ref>