# 分块矩阵

${\displaystyle \mathbf {A} ={\begin{bmatrix}1&2\\3&4\end{bmatrix}}}$

## 范例

${\displaystyle P={\begin{bmatrix}1&1&2&2\\1&1&2&2\\3&3&4&4\\3&3&4&4\end{bmatrix}}}$

${\displaystyle P_{11}={\begin{bmatrix}1&1\\1&1\end{bmatrix}},P_{12}={\begin{bmatrix}2&2\\2&2\end{bmatrix}},P_{21}={\begin{bmatrix}3&3\\3&3\end{bmatrix}},P_{22}={\begin{bmatrix}4&4\\4&4\end{bmatrix}}}$

## 分块矩阵乘法

${\displaystyle \mathbf {A} ={\begin{bmatrix}\mathbf {A} _{11}&\mathbf {A} _{12}&\cdots &\mathbf {A} _{1s}\\\mathbf {A} _{21}&\mathbf {A} _{22}&\cdots &\mathbf {A} _{2s}\\\vdots &\vdots &\ddots &\vdots \\\mathbf {A} _{q1}&\mathbf {A} _{q2}&\cdots &\mathbf {A} _{qs}\end{bmatrix}}}$

${\displaystyle \mathbf {B} ={\begin{bmatrix}\mathbf {B} _{11}&\mathbf {B} _{12}&\cdots &\mathbf {B} _{1r}\\\mathbf {B} _{21}&\mathbf {B} _{22}&\cdots &\mathbf {B} _{2r}\\\vdots &\vdots &\ddots &\vdots \\\mathbf {B} _{s1}&\mathbf {B} _{s2}&\cdots &\mathbf {B} _{sr}\end{bmatrix}},}$

${\displaystyle \mathbf {C} =\mathbf {A} \mathbf {B} }$

${\displaystyle \mathbf {C} _{\alpha \beta }=\sum _{\gamma =1}^{s}\mathbf {A} _{\alpha \gamma }\mathbf {B} _{\gamma \beta }}$