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A rotation corresponds to an orthogonal matrix with determinant +1. If you insist on having a proper rotation, you can simply combine the reflection above with another reflection that leaves both vectors fixed: the product of two reflections is a rotation. Oct 01, 2015 · This was rediscovered independently by Rodrigues in 1840 with Rodrigues parameters of tangent of half the rotation angle attached with coordinates of the rotation axis, known as Rodrigues vector , , sometimes called the vector–parameter , presenting a way for geometrically constructing a rotation matrix. The vector form of this formula was ...

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