In the inversion operation for 3D coordinates, the inversion center is the origin ( 0, 0, 0 ).
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However, due to the high complexity of the matrix-inversion operation, computing the pseudoinverse in high-dimensional cases is in many cases intractable.
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A Lie group is " C " " manifold that also carries a group structure whose product and inversion operations are smooth as maps of manifolds.
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The set of invertible elements in any unital Banach algebra is an open set, and the inversion operation on this set is continuous, ( and hence homeomorphism ) so that it forms a topological group under multiplication.
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Following Lewin's revival ( in GMIT ) of Hugo Riemann's three contextual inversion operations on triads ( relative, and Leittonwechsel ) as formal transformations, the branch of transformation theory called Neo-Riemannian theory was popularized by Brian Hyer ( 1995 ), Michael Kevin Mooney ( 1996 ), Richard Cohn ( 1997 ), and an entire issue of the " Journal of Music Theory " ( 42 / 2, 1998 ).
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