Attitude and orbit error in n-dimensional spaces
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This paper focuses the attention on theoretical aspects associated with the definition of the error for Special Orthogonal and for General Linear transformations, in any dimensional space, Real or Complex, and in both Euclidean and Riemannian spaces. In particular, the paper shows that the orbit error can be described by a complex number whose phase represents the orbit orientation error while the modulus describes the orbit shape error. This paper also shows that the angle between two quaternion has a specific geometrical meaning. In particular, the QR decomposition allows us to see a General Linear transformation as made of two subsequent effectsia dilation and a rigid rotation. This decomposition has been applied to the Lorentz transformations by highlighting the relativity effects of length change and coordinate axes bending.
