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Lattices under linear transformation
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2-dimensional A(Sf admissible lattice arbitrarily small automorph boundary of Jf boundary point bounded bounded set Cassels Chapter clearly co-ordinates coefficients concludes the proof continued fractions contradiction convex body theorem convex set convex symmetric Corollary critical lattice Davenport defined definite quadratic form denote determinant distance function distance-function equivalent euclidean space exist finite number follows at once Geometry of Numbers given Hence homogeneous linear transformation hyperplane inequality infimum infinitely integers lattice constant Lemma Let F(x linearly independent points Mahler Minkowski-Hlawka Theorem Minkowski's convex body Minkowski's theorem Mordell non-singular packing parallelogram parallelopiped point of Sf point x0 positive number proof of Theorem properties proportional to integral quotient space real numbers result Rogers satisfies sequence set of points set Sf shape sphere star-body successive minima suppose without loss symmetric convex tac-plane Theorem IV Theorem VII trivial V(Sf values vectors volume