LA.Ch6.Ex7.NEW.Seongchan

2070 days ago by seongchan

x1,x2,x3,x4=var('x1 x2 x3 x4') SM_T1(x1,x2,x3,x4)=(2*x1-x4,-x1+x2,-x1-3*x2+5*x3,-4*x1-2*x3+3*x4) SM_T2(x1,x2,x3,x4)=(x1+2*x2-x3,x2-x3+3*x4,-2*x4,x1-x4) T1=linear_transformation(QQ^4, QQ^4,SM_T1) T2=linear_transformation(QQ^4, QQ^4,SM_T2) M_T1 = T1.matrix(side='right') M_T2 = T2.matrix(side='right') print "[T1] = \n",M_T1 print "[T2] = \n",M_T2 print "[T2*T1] = \n",M_T2*M_T1 print "[T1*T2]= \n",M_T1*M_T2 
       
[T1] = 
[ 2  0  0 -1]
[-1  1  0  0]
[-1 -3  5  0]
[-4  0 -2  3]
[T2] = 
[ 1  2 -1  0]
[ 0  1 -1  3]
[ 0  0  0 -2]
[ 1  0  0 -1]
[T2*T1] = 
[  1   5  -5  -1]
[-12   4 -11   9]
[  8   0   4  -6]
[  6   0   2  -4]
[T1*T2]= 
[  1   4  -2   1]
[ -1  -1   0   3]
[ -1  -5   4 -19]
[ -1  -8   4   1]
[T1] = 
[ 2  0  0 -1]
[-1  1  0  0]
[-1 -3  5  0]
[-4  0 -2  3]
[T2] = 
[ 1  2 -1  0]
[ 0  1 -1  3]
[ 0  0  0 -2]
[ 1  0  0 -1]
[T2*T1] = 
[  1   5  -5  -1]
[-12   4 -11   9]
[  8   0   4  -6]
[  6   0   2  -4]
[T1*T2]= 
[  1   4  -2   1]
[ -1  -1   0   3]
[ -1  -5   4 -19]
[ -1  -8   4   1]