Lattices in Computer Science Lecture 8 Dual Lattices Lecturer : Oded Regev Scribe : Gillat Kol
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چکیده
From the above definition, we have the following geometrical interpretation of the dual lattice. For any vector x, the set of all points whose inner product with x is integer forms a set of hyperplanes perpendicular to x and separated by distance 1/‖x‖. Hence, any vector x in a lattice Λ imposes the constraint that all points in Λ∗ lie in one of the hyperplanes defined by x. See the next figure for an illustration.
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