๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

A Note on lattices of euclidean subspaces

โœ Scribed by Ton Geerts

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
256 KB
Volume
31
Category
Article
ISSN
0005-1098

No coin nor oath required. For personal study only.

โœฆ Synopsis

Any nonvoid lattice of subspaces from R" is known to be a complete lattice, and hence it has a largest and smallest element. Here we show that for a specific class of subspaces also the converse is true. If this class has a largest and a smallest element, then it is a complete lattice. Within the context of algebraic Riccati equations, it follows that the usual classes of real symmetric and positive semidefinite solutions are lattices if and only if these classes contain extremal elements, and if this is the case, then these lattices are modular, yet not necessarily distributive, as is demonstrated by a counterexample.

๐Ÿ“œ SIMILAR VOLUMES

A Note on Optimal Unimodular Lattices
A Note on Optimal Unimodular Lattices
โœ J.H Conway; N.J.A Sloane ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 169 KB

The highest possible minimal norm of a unimodular lattice is determined in dimensions n 33. There are precisely five odd 32-dimensional lattices with the highest possible minimal norm (compared with more than 8.10 20 in dimension 33). Unimodular lattices with no roots exist if and only if n 23, n{25

A note on solving multifacility location
A note on solving multifacility location problems involving euclidean distances
โœ Henrik Juel ๐Ÿ“‚ Article ๐Ÿ“… 1982 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 121 KB

## Abstract This note considers a recently proposed solution method for a multifacility location problem. It is shown that the method does not always produce an optimal solution.

On the Geometricity of Lattices Generate
On the Geometricity of Lattices Generated by Orbits of Subspaces Under Finite Classical Groups
โœ Yuanji Huo; Zhe-Xian Wan ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 165 KB

Let n q be the n-dimensional vector space over the finite field q and let G n be one of the classical groups of degree n over q . Let be any orbit of subspaces under G n . Denote by the set of subspaces which are intersections of subspaces in and assume the intersection of the empty set of subspaces