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Finding correspondences between feature points is one of the most relevant problems in the whole set of visual tasks. In this paper we address the problem of matching a feature vector (or a matrix) to a given subspace. Given any vector base of such a subspace, we observe a linear combination of its elements with all entries swapped by an unknown permutation. We prove that such a computationally hard integer problem is uniquely solved in a convex set resulting from relaxing the original problem. Also, if noise is present, based on this result, we provide a robust estimate recurring to a linear programming-based algorithm. We use structure-from-motion and object recognition as motivating examples.