@interact
def linear_transformation(A=matrix([[1,-1],[-1,1/2]]),theta=slider(0, 2*pi, .1), r=slider(0.1, 2, .1, default=1)):
v=vector([r*cos(theta), r*sin(theta)])
w = A*v
circles = sum([circle((0,0), radius=i, color='black') for i in [1..2]])
html("$%s %s=%s$"%tuple(map(latex, [A, v.column().n(4), w.column().n(4)])))
show(v.plot(color='red')+w.plot(color='blue')+circles,aspect_ratio=1)
