一、矩阵和向量的乘积
$Aoldsymbol x=left[ egin{array}{cc}a _{1,1}&a_{1,2}\a_{2,1}&a_{2,2} end{array} ight]left[ egin{array}{cc}x_1\x_2 end{array} ight]=left[ egin{array}{cc}a _{1,1}\a_{2,1} end{array} ight]x_1+left[egin{array}{cc}a _{1,1}\a_{2,1} end{array} ight]x_2= left[ egin{array}{cc}a_{1,1}x_1+a_{1,2}x_2\a_{2,1}x_1+a_{2,2}x_2end{array} ight]$
口诀：列同入，行同出。第$j$列的元素都是和第$j$个输入变量相乘，第$i$行的元素都是输出到第$i$个输出变量
二、矩阵和矩阵的乘积
$AX=Aleft[egin{array}{cc} oldsymbol x_1 & oldsymbol x_2 end{array} ight]=left[egin{array}{cc} Aoldsymbol x_1 & Aoldsymbol x_2 end{array} ight]$
可以用分块矩阵理解上述式子：$A$是$1 imes 1$块，$X$是$1 imes 2$块，所以结果是$1 imes 2$块