Block matrix/2x2/Definition

A block matrix is an ${\displaystyle {}m\times n}$-matrix of the form

${\displaystyle {\begin{pmatrix}A&B\\C&D\end{pmatrix}},}$

where ${\displaystyle {}A}$ is an ${\displaystyle {}r\times s}$-matrix, ${\displaystyle {}B}$ is an ${\displaystyle {}r\times (n-s)}$-matrix, ${\displaystyle {}C}$ is an ${\displaystyle {}(m-r)\times s}$-matrix and ${\displaystyle {}D}$ is an ${\displaystyle {}(m-r)\times (n-s)}$-matrix.