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Solve Matrix A = B for variables a b and c with equations consisting of cosines and sines

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Stijn Klevering
Stijn Klevering 2018-2-20
编辑： Matt J 2018-2-20
What is the easiest way to solve A = B for a, b and g with the following matrices:
A = [ cos(b)*cos(g), cos(g)*sin(a)*sin(b) - cos(a)*sin(g), sin(a)*sin(g) + cos(a)*cos(g)*sin(b); cos(b)*sin(g), sin(a)*sin(b)*sin(g) - cos(a)*cos(g), cos(g)*sin(a) + cos(a)*sin(b)*sin(g);
-sin(b), cos(b)*sin(a), cos(a)*cos(b)]
B = [0.6122, -0.7891, -0.0506;
0.7903, 0.6126, 0.0091;
-0.0238, 0.0456, -0.9987]
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Matt J
Matt J 2018-2-20
编辑：Matt J 2018-2-20
Like I said, you will find code routines to do these kind of decompositions for you on the File Exchange. No need to re-invent the wheel. I don't think you will be able to solve it symbolically, because your B is not precisely orthogonal. It contains floating point errors.
John D'Errico
John D'Errico 2018-2-20
You want to solve for A==B. That is equivalent to having 9 simultaneous equations.
You have THREE variables. Nine equations. There are too many equations in only 3 unknowns.
There will essentially never be an exact solution. This is why solve could not succeed.

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