x, y, z = var('x, y, z')
h(x, y, z) = [-x-6*z,3*x+4*z,-2*x+5*y]
T = linear_transformation(QQ^3, QQ^3, h)
x1=vector([1,0,0])
x2=vector([0,0,1])
x3=vector([1,1,0])
y1=vector([2,0])
y2=vector([0,1])
B=column_matrix([x1, x2, x3, T(x1), T(x2), T(x3)])
print B
print
C=B.echelon_form()
print C
print
A=C.submatrix(0, 3, 3, 3)
print A
print
P=matrix(3,3,[0,-3,3,-1,3,2,0,1,-3])
print P
print
P1=P.inverse()
print P1
print
print P1*A*P
|
|
[ 1 0 1 -1 -6 -1]
[ 0 0 1 3 4 3]
[ 0 1 0 -2 0 3]
[ 1 0 0 -4 -10 -4]
[ 0 1 0 -2 0 3]
[ 0 0 1 3 4 3]
[ -4 -10 -4]
[ -2 0 3]
[ 3 4 3]
[ 0 -3 3]
[-1 3 2]
[ 0 1 -3]
[-11/6 -1 -5/2]
[ -1/2 0 -1/2]
[ -1/6 0 -1/2]
[-25/3 49/3 95/3]
[ -3 8 6]
[ 1/3 2/3 -2/3]
[ 1 0 1 -1 -6 -1]
[ 0 0 1 3 4 3]
[ 0 1 0 -2 0 3]
[ 1 0 0 -4 -10 -4]
[ 0 1 0 -2 0 3]
[ 0 0 1 3 4 3]
[ -4 -10 -4]
[ -2 0 3]
[ 3 4 3]
[ 0 -3 3]
[-1 3 2]
[ 0 1 -3]
[-11/6 -1 -5/2]
[ -1/2 0 -1/2]
[ -1/6 0 -1/2]
[-25/3 49/3 95/3]
[ -3 8 6]
[ 1/3 2/3 -2/3]
|