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矩陣乘法結合律的證明 矩陣乘法結合律分配律

a==(a i j),b=(bij),c=(cij),ab=(dij),bc=(eij),ab=(cij),ab=(dij),bc=(eij),(ab)c=(fij),a(bc)=(gij)!a i

a==(a i j),b=(bij),c=(cij),ab=(dij),bc=(eij),ab=(cij),ab=(dij),bc=(eij),(ab)c=(fij),a(bc)=(gij)

!a i n*bnj,i,j=1,2,…,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,n,艾因*恩杰,我,J=1,2,…,N,

!DIN*CNJ

=(AI1*B11 AI2*B21…AIN*BN1)*C1J(AI1*B11 AI2*B21…AIN*BN1)*C2J…(AI1*B1N AI2*B2N…AIN*BNN)*CNJ

=AI1(B11*C1J B12*C2J…B1N*CNJ)AI2(B21*C1J B22*C2J…[中國解釋]AIN(BN1*C1J BN2*C2J…BNN*CNJ)=AI1*E1J AI2*E1J AI2*E1J AI2*E2J*E2J*E2J*E2J*E2J*E2J*E2J*E2J*E2JA=B=C=A(B)!~!X Y=Y X

XY=YX

Y X=Y ^ 2 X(Y-X)

Y X=Y ^ 2 Y(Y-X)!XY-YX=X ^ 2 Y ^ 2-(X-Y)^ 2

XY-YX=2XY]∴