定义 1.6. (矩阵乘法)

设矩阵 $A = (a_{ij})_{s n}, B = (b_{k l})_{nm}$ ，则矩阵

C = (c_{ij})_{s m} = c_{11} c_{21} ⋮ c_{s 1} c_{12} c_{22} ⋮ c_{s 2} \dots \dots \dots c_{1 m} c_{2 m} ⋮ c_{s m}

称为矩阵 $A$ 与 $B$ 的乘积, 其中

c_{ij} = a_{i 1} b_{1 j} + a_{i 2} b_{2 j} + \dots + a_{in} b_{nj} = k = 1 \sum n a_{ik} b_{kj} (i = 1, 2, \dots, s; j = 1, 2, \dots, m)

记作 $C = A B$ .

Youliang Zhong