矩阵乘法：
输入两个可以相乘的矩阵，每个元用逗号隔开，每行用分号结尾。
注意，不支持支持数学函数和变量。
输入两个可以相乘的矩阵，每个元用逗号隔开，每行用分号结尾。
注意，不支持支持数学函数和变量。
当前位置：线性代数 >矩阵乘法 >矩阵乘法计算历史
$$\begin{aligned}&\\ \color{black}{计算矩阵}& \color{black}{\ \ \begin{pmatrix} &1\ &8\ &6\ &9\ &3\ &6\ &8\ &4\ \\ &7\ &3\ &6\ &2\ &1\ &7\ &5\ &8\ \\ &2\ &8\ &6\ &9\ &4\ &5\ &2\ &1\ \\ &4\ &2\ &9\ &7\ &7\ &6\ &8\ &2\ \\ &1\ &8\ &3\ &8\ &5\ &9\ &4\ &2\ \\ &9\ &5\ &9\ &4\ &3\ &7\ &4\ &2\ \\ &3\ &9\ &6\ &4\ &3\ &9\ &6\ &5\ \\ &1\ &5\ &3\ &8\ &6\ &4\ &2\ &8\ \end{pmatrix}\times \begin{pmatrix} &1\ &8\ &6\ &9\ &3\ &6\ &8\ &4\ \\ &7\ &3\ &6\ &2\ &1\ &7\ &5\ &8\ \\ &2\ &8\ &6\ &9\ &4\ &5\ &2\ &1\ \\ &4\ &2\ &9\ &7\ &7\ &6\ &8\ &2\ \\ &1\ &8\ &3\ &8\ &5\ &9\ &4\ &2\ \\ &9\ &5\ &9\ &4\ &3\ &7\ &4\ &2\ \\ &3\ &9\ &6\ &4\ &3\ &9\ &6\ &5\ \\ &1\ &5\ &3\ &8\ &6\ &4\ &2\ &8\ \end{pmatrix}}\\ \end{aligned}$$
$$\begin{aligned}&\\ \color{black}{计算矩阵}& \color{black}{\ \ \begin{pmatrix} &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ \\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ \\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ \\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ \\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ \end{pmatrix}\times \begin{pmatrix} &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ \\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ \\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ \\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ \\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ \end{pmatrix}}\\ \end{aligned}$$
$$\begin{aligned}&\\ \color{black}{计算矩阵}& \color{black}{\ \ \begin{pmatrix} &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ \\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ \\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ \\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ \end{pmatrix}\times \begin{pmatrix} &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ \\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ \\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ \\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ \end{pmatrix}}\\ \end{aligned}$$
$$\begin{aligned}&\\ \color{black}{计算矩阵}& \color{black}{\ \ \begin{pmatrix} &0\ \\ &21\ \end{pmatrix}\times \begin{pmatrix} &0\ &21\ \end{pmatrix}}\\ \end{aligned}$$
$$\begin{aligned}&\\ \color{black}{计算矩阵}& \color{black}{\ \ \begin{pmatrix} &1\ &1\ &1\ &1\ \\ &1\ &1\ &1\ &1\ \\ &1\ &1\ &1\ &1\ \\ &1\ &1\ &1\ &1\ \end{pmatrix}\times \begin{pmatrix} &1\ &1\ &1\ &1\ \\ &1\ &1\ &1\ &1\ \\ &1\ &1\ &1\ &1\ \\ &1\ &1\ &1\ &1\ \end{pmatrix}}\\ \end{aligned}$$
首页 << 第103页 第104页 第105页 第106页 第107页 第108页 第109页 >> 尾页 共109页
$$\begin{aligned}&\\ \color{black}{计算矩阵}& \color{black}{\ \ \begin{pmatrix} &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ \\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ \\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ \\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ \\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ \end{pmatrix}\times \begin{pmatrix} &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ \\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ \\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ \\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ \\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ &\frac{1}{5}\ \end{pmatrix}}\\ \end{aligned}$$
$$\begin{aligned}&\\ \color{black}{计算矩阵}& \color{black}{\ \ \begin{pmatrix} &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ \\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ \\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ \\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ \end{pmatrix}\times \begin{pmatrix} &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ \\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ \\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ \\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ &\frac{1}{4}\ \end{pmatrix}}\\ \end{aligned}$$
$$\begin{aligned}&\\ \color{black}{计算矩阵}& \color{black}{\ \ \begin{pmatrix} &0\ \\ &21\ \end{pmatrix}\times \begin{pmatrix} &0\ &21\ \end{pmatrix}}\\ \end{aligned}$$
$$\begin{aligned}&\\ \color{black}{计算矩阵}& \color{black}{\ \ \begin{pmatrix} &1\ &1\ &1\ &1\ \\ &1\ &1\ &1\ &1\ \\ &1\ &1\ &1\ &1\ \\ &1\ &1\ &1\ &1\ \end{pmatrix}\times \begin{pmatrix} &1\ &1\ &1\ &1\ \\ &1\ &1\ &1\ &1\ \\ &1\ &1\ &1\ &1\ \\ &1\ &1\ &1\ &1\ \end{pmatrix}}\\ \end{aligned}$$
首页 << 第103页 第104页 第105页 第106页 第107页 第108页 第109页 >> 尾页 共109页
矩阵乘法的性质：
（i）结合律： ( A B ) C = A ( B C ) 。
（ii）分配律： A ( B + C ) = A B + A C 或者 ( A + B ) C = A C + B C 。
（iii） λ ( A B ) = ( λ A ) B = A ( λ B ) 。
其中，A、B、C是使上述矩阵乘法有意义的矩阵，λ是数。