math

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import matplotlib.pyplot as plt
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import math
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import numpy as np
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fig = plt.figure()
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ax = fig.add_subplot(1,1,1)
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ax.spines['left'].set_position('zero')
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ax.spines['bottom'].set_position('zero')
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ax.spines['right'].set_color('none')
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ax.spines['top'].set_color('none')
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plt.axis('scaled')
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plt.xlim(-2, 5)
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plt.ylim(-5, 8)
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alfa = math.pi / 4
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d1, d2 = np.array([2, 2]), np.array([-1, 1])
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A = np.array([ d1, d2 ]).transpose()
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x, y =  3, -3
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v = np.array([x, y])
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w = np.dot (A,v)
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print (A)
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X, Y = w[0], w[1]
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ax.arrow(0, 0, X, Y, head_width=0.15, head_length=0.2, length_includes_head=True, facecolor='green')
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ax.arrow(0, 0, x, y, head_width=0.15, head_length=0.2, length_includes_head=True, facecolor='black')
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plt.show()
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A1 = np.linalg.inv(A)
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print(np.dot (A1,v))