Harmonic Analysis on So(3)

نویسنده

  • CHRISTIAN REMLING
چکیده

Such a rotation g can be described by three parameters. For instance, if you know the axis of rotation (specified by a direction or a point on S or two angles) and the angle of rotation (one parameter), g is determined uniquely. Alternatively, a matrix g ∈ R3×3 has 9 entries, but the requirement that gg = 1 gives 6 conditions on these entries, and again 9− 6 = 3. (The condition that det g = 1 singles out one half of the matrices satisfying gg = 1; it does not reduce the dimension.) Summarizing in fancy language and adding some precision, we have:

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تاریخ انتشار 2005