0 思维导图
一、矩阵分块法介绍
5.1 概念
对于行数和列数比较多的矩阵A,运算时常采用分块法,
使大的矩阵运算化成小的矩阵运算.将矩阵A用若干个纵线和横线分小矩阵,每一个
小矩阵称为矩阵A的子块,以子块为元素的形式上的矩阵称为分块矩阵
例
例如将 3 × 4 矩阵 A = ( a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 a 31 a 32 a 33 a 34 ) 分成以下三种形式: ( 1 ) ( a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 a 31 a 32 a 33 a 34 ) , ( 2 ) ( a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 a 31 a 32 a 33 a 34 ) ( 3 ) ( a 11 a 12 a 13 a 14 a 21 a 22 a 23 a 24 a 31 a 32 a 33 a 34 ) . 其中 A 11 = ( a 11 a 12 a 21 a 22 ) , A 12 = ( a 13 a 14 a 23 a 24 ) , A 21 = ( a 31 a 32 ) , A 22 = ( a 33 a 34 ) , \begin{aligned} &例如将3×4矩阵 \\ &\left.A=\left(\begin{array}{llll}{ {a_{11}}}&{ {a_{12}}}&{ {a_{13}}}&{ {a_{14}}}\\{ {a_{21}}}&{ {a_{22}}}&{ {a_{23}}}&{ {a_{24}}}\\{ {a_{31}}}&{ {a_{32}}}&{ {a_{33}}}&{ {a_{34}}}\end{array}\right.\right) \\ &\text{分成以下三种形式:} \\ &(1)\quad\left(\begin{array}{cc:cc}a_{11}&a_{12}&a_{13}&a_{14}\\a_{21}&a_{22}&a_{23}&a_{24}\\\hdashline a_{31}&a_{32}&a_{33}&a_{34}\end{array}\right),\quad(2)\quad\left(\begin{array}{ccc|c}a_{11}&a_{12}&a_{13}&a_{14}\\a_{21}&a_{22}&a_{23}&a_{24}\\\hdashline a_{31}&a_{32}&a_{33}&a_{34}\end{array}\right) \\ &(3)\quad\left(\begin{array}{c:c:c:c}{ {a_{11}}}&{ {a_{12}}}&{ {a_{13}}}&{ {a_{14}}}\\{ {a_{21}}}&{ {a_{22}}}&{ {a_{23}}}&{ {a_{24}}}\\{ {a_{31}}}&{ {a_{32}}}&{ {a_{33}}}&{ {a_{34}}}\end{array}\right). \\ &\text{其中} \\ &A_{11}=\left(\begin{array}{cc}{ {a_{11}}}&{ {a_{12}}}\\{ {a_{21}}}&{ {a_{22}}}\end{array}\right),\quad A_{12}=\left(\begin{array}{cc}{ {a_{13}}}&{ {a_{14}}}\\{ {a_{23}}}&{ {a_{24}}}\end{array}\right), \\ &\text{} A_{21}=\left(\begin{array}{cc}{ {a_{31}}}&{ {a_{32}}}\end{array}\right),\quad A_{22}=\left(\begin{array}{cc}{ {a_{33}}}&{ {a_{34}}}\end{array}\right), \\ &\text{} \end{aligned} 例如将3×4矩阵A= a11a21a31a12a22a32a13a23a33a14a24a34 分成以下三种形式:(1) a11a21a
