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Results tagged with lattices
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user 48609
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])
1
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shortest lattice point solution to a linear system
Consider the lattice $\mathbb{Z}^n$ and a real matrix $A\in \mathbb{R}^{m\times n}$ ($m<n$) with orthonormal rows. Let $y\in A\mathbb{Z}^n\setminus\{0\}$ and consider the equation $Ax=y$. Is there a ( …
- 640
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answer
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lattice orthogonal complement
Let $A\in \mathbb{Z}^{m\times n}$ ($m<n$) be a matrix with orthogonal rows. Further assume that the gcd of the coefficients in each row of $A$ is $1$.
Consider $\ker A\cap \mathbb{Z}^n = \{x\in\math …
- 640