多次线性变换等价于矩阵连乘 1=411x1+412X2+a3X3 ·设 y2=a21x+a22X2+a23X3 写成Y=AX x1=b41+b2t2 ·及 x2=b241+b22t2 写成X=BT x3=b3141+b32t2 则有： a11 a12 名 Y= =ABT a22多次线性变换等价于矩阵连乘 • 设 写成Y=AX • 及 写成Ｘ=BT • 则有： 1 11 1 12 2 13 3 2 21 1 22 2 23 3 y a x a x a x y a x a x a x  = + +   = + + 1 11 1 12 2 2 21 1 22 2 3 31 1 32 2 x b t b t x b t b t x b t b t  = +   = +   = + 11 12 11 12 13 1 21 22 21 22 23 2 31 32 b b a a a t b b a a a t b b         = =               Y ABT