Definition:Point Lattice/Definition 2
Jump to navigation
Jump to search
Definition
Let $\R^m$ be the $m$-dimensional real Euclidean space.
Let $\set {\mathbf v_1, \mathbf v_2, \ldots, \mathbf v_n}$ be a linearly independent set of vectors of $\R^m$.
A point lattice in $\R^m$ is the set of all integer linear combinations of such vectors.
That is:
- $\ds \map \LL {\mathbf v_1, \mathbf v_2, \ldots, \mathbf v_n} = \set {\sum_{i \mathop = 1}^n a_i \mathbf v_i : a_i \in \Z}$
Also known as
A point lattice is also known just as a lattice, but that term has more than one meaning.
Hence point lattice is what is to be used on $\mathsf{Pr} \infty \mathsf{fWiki}$ for this concept.
Also see
- Results about point lattices can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): lattice: 2. (in geometry; C.F. Gauss, 1831)
- 2002: Daniele Micciancio and Shafi Goldwasser: Complexity of Lattice Problems: A Cryptographic Perspective: $\S 1$
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): lattice: 2. (in geometry; C.F. Gauss, 1831)