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Transformation matrix
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===Rotation=== The [[rotation matrix#General 3D rotations|matrix to rotate]] an angle ''ΞΈ'' about any axis defined by [[unit vector]] (''x'',''y'',''z'') is<ref>{{cite book |page = 154 |title = Basic Mathematics for Electronic Engineers:Models and Applications |first = John E. |last = Szymanski |publisher = Taylor & Francis |year = 1989 |isbn = 0278000681 }}</ref> <math display="block">\begin{bmatrix} xx(1-\cos \theta)+\cos\theta & yx(1-\cos\theta)-z\sin\theta & zx(1-\cos\theta)+y\sin\theta\\ xy(1-\cos\theta)+z\sin\theta & yy(1-\cos\theta)+\cos\theta & zy(1-\cos\theta)-x\sin\theta \\ xz(1-\cos\theta)-y\sin\theta & yz(1-\cos\theta)+x\sin\theta & zz(1-\cos\theta)+\cos\theta \end{bmatrix}.</math>
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