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Results tagged with lattices
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user 44293
Lattices in the sense of discrete subgroups of Euclidean spaces, as used in number theory, discrete geometry, Lie groups, etc. (Not to be confused with lattice theory or lattices as used in physics! For lattices (ordered sets), use the tag: [lattice-theory])
3
votes
Bound on Minimal Length of Vectors in Lattice and its Dual Lattice
The product $d\times d^*$ cannot be "so" large, as a consequence of the so-called Transference theorems Particularly, Thm. 2.1. of the paper shows that $d\times d^* \leq n^2$ (hence in your example, …
- 800
2
votes
Accepted
Covolume of the row span of a matrix and of the kernel of a matrix
From this characeterisation (p.166 of Conway and Sloane's book 1), we show that $\sqrt{\det(V_1 V_1^t)} = \mbox{CoVol}(\ker(\phi_A))$.
1 Sphere Packings, Lattices and Groups, 3rd Ed. …
- 800