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I have an orthogonalized rotation matrix

-0.500000 -0.866025 0.000000

0.866025 -0.500000 0.000000

0.000000 0.000000 1.000000

for the following unit cell:

a b c alpha beta gamma space group

131.760 131.760 120.910 90.00 90.00 120.00 P 31

Does anyone know how I convert my original rotation matrix to the following one for operation on on a set of fractional coordinates?

0.000000 -1.000000 0.000000

1.000000 -1.000000 0.000000

0.000000 0.000000 1.000000

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# Converting Rotation matrix to operate on fractional coordinates

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