分块矩阵 (block matrix)

标量

$(a_{1} a_{2}) (b_{1} b_{2})$

奇怪的乘法

$(a_{1} a_{2}) (b_{1} b_{2}) = (a_{1} b_{1} a_{2} b_{1} a_{1} b_{2} a_{2} b_{2})$

分块

只要证明

$(A C B D) (E G F H) = (A E + BG CE + D G A F + B H CF + DH)$

即可，

$(a_{11} a_{21} a_{12} a_{22}) (b_{11} b_{21} b_{12} b_{22}) = (() \cdot () () \cdot () () \cdot () () \cdot ())$