v_1: (1, 2)
v_2: (1, -1)
e_1: (1, 0)
e_2: (0, 1)
c_1 = 1.45 (slider from -5 to 5, step 0.01)
c_2 = 1 (slider from -5 to 5, step 0.01)
c: (c_1, c_2)
v: (c_1 * v_1) + (c_2 * v_2)
P: {{1, 1}, {2, -1}}
s = 1 (slider from -5 to 5, step 0.05)
w: ((s * P) * c)
d: (Invert[P] * w)