disp("Kanonical Basis")

e1 = [1 0 0]'
e2 = [0 1 0]'
e3 = [0 0 1]'

E = [e1 e2 e3]

A = [1 2 3; 4 5 6]

disp("This defines a lin. transf. L(v) = A*v")


disp("The columns of A are the images of the basis verctors")
disp("Image of basis vector e1: b1 = L(e1)=A*e1")
b1 = A*e1

disp("Image of basis vector e2: b2 = L(e2)=A*e2")
b2 = A*e2

disp("Image of basis vector e3: b3 = L(e3)=A*e3")
b3 = A*e3

disp("v = 2*e1 + 3*e2 + 4*e3")
v = 2*e1 + 3*e2 + 4*e3 

disp("w=L(v)=A*v = L(2*e1+3*e2+4*e3)")
w = A*v

disp("w=2*L(e1)+3*L(e2)+4*L(e3)")
ww = 2*b1 + 3*b2 + 4*b3