参考
mathsisfun matrix multiplying 数学乐 矩阵乘法 edu-edu矩阵乘法
Illustration
The figure to the right illustrates diagrammatically the product of two matrices A and B, showing how each intersection in the product matrix corresponds to a row of A and a column of B.
[ a 11 a 12 ⋅ ⋅ a 31 a 32 ⋅ ⋅ ] 4 × 2 matrix [ ⋅ b 12 b 13 ⋅ b 22 b 23 ] 2 × 3 matrix = [ ⋅ c 12 c 13 ⋅ ⋅ ⋅ ⋅ c 32 c 33 ⋅ ⋅ ⋅ ] 4 × 3 matrix {\displaystyle {\overset {4\times 2{\text{ matrix}}}{\begin{bmatrix}{a_{11}}&{a_{12}}\\\cdot &\cdot \\{a_{31}}&{a_{32}}\\\cdot &\cdot \\\end{bmatrix}}}{\overset {2\times 3{\text{ matrix}}}{\begin{bmatrix}\cdot &{b_{12}}&{b_{13}}\\\cdot &{b_{22}}&{b_{23}}\\\end{bmatrix}}}={\overset {4\times 3{\text{ matrix}}}{\begin{bmatrix}\cdot &c_{12}&c_{13}\\\cdot &\cdot &\cdot \\\cdot &c_{32}&c_{33}\\\cdot &\cdot &\cdot \\\end{bmatrix}}}} a 11 ⋅ a 31 ⋅ a 12 ⋅ a 32 ⋅ 4 × 2 matrix [ ⋅ ⋅ b 12 b 22 b 13 b 23 ] 2 × 3 matrix = ⋅ ⋅ ⋅ ⋅ c 12 ⋅ c 32 ⋅ c 13 ⋅ c 33 ⋅ 4 × 3 matrix The values at the intersections marked with circles are:
c 12 = a 11 b 12 + a 12 b 22 c 33 = a 31 b 13 + a 32 b 23 {\displaystyle {\begin{aligned}c_{12}&={a_{11}}{b_{12}}+{a_{12}}{b_{22}}\\c_{33}&={a_{31}}{b_{13}}+{a_{32}}{b_{23}}\end{aligned}}} c 12 c 33 = a 11 b 12 + a 12 b 22 = a 31 b 13 + a 32 b 23 图示如下：
应用（Fundamental applications）
