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The closest point of a linear variety to an external point is found by usingthe equality case of an Ostrowski's type inequality. This point is given inclosed form as the quotient of a (formal) and a (scalar) Gram determinant.Then, the best approximation pair of points onto two linear varieties is given,as well as characterization of this pair of best approximation points.

Best Approximation Pair of Two Linear Varieties via an (In)Equality by (Fan-Todd) Beesack