High Quality Content by WIKIPEDIA articles! The orthogonal Procrustes problem is a matrix approximation problem in linear algebra. In its classical form, one is given two matrices A and B and asked to find an orthogonal matrix R which most closely maps A to B. Specifically, R = argmin_Omega |AOmega-B|_F quadmathrm{subject to}quad Omega^T Omega=I, where |cdot|_F denotes the Frobenius norm. There are a number of related problems to the classical orthogonal Procrustes problem. One might generalize it by seeking the closest matrix in which the columns are orthogonal, but not necessarily orthonormal. Alternately, one might constrain it by only allowing rotation matrices with determinant 1 (special orthogonal matrices) In this case, one can write (using the above decomposition M = U?V * )

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