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As often in math, trap is too think something is obvious ! True formula to go from one image to the other is

K @ rot15 @ rot10.T @ inv(K)

as K is diagonal I assumed that it has no effect but when I made the entire computation I found

K @ rot15 @ rot10.T @ np.linalg.inv(K)
Out[197]: 
array([[ 9.96199327e-01, -7.55452868e-02,  1.73427108e+01],
       [ 7.54128878e-02,  9.97141394e-01,  1.87342755e+00],
       [-1.08966647e-04, -3.49027100e-06,  9.99048675e-01]])

and that is H :))

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