Let [A 1 , ..., A m ] be a set of m matrices of size n\_n over the field F such that A i # SL(n, F) for 1 i m and such that A i &A j # SL(n, F) for 1 i< j m. The largest integer m for which such a set exists is called the Parsons number for n and F, denoted m(n, F). We will call such a set of m(n, F
Compound and unimodular matrices
โ Scribed by David P. Brown
- Publisher
- Elsevier Science
- Year
- 1977
- Tongue
- English
- Weight
- 560 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
โฆ Synopsis
if P is any square unimodular matrax of order n. it is proven that the n .-f coqwund of ,fJ, pw U, is unimodular. If P is rectangular of order n x +I. unimodular matrices c~f t)rder k + I lln PC" are chatact&ted. A sign rule for P"', n 5 I:I, Is estabiished. fat certain pairs of rows in P"". ahe product of the elements in each column is a;lways either -i,CI or always -1,O.
๐ SIMILAR VOLUMES
Conference matrices are used to define complex structures on real vector spaces. Certain lattices in these spaces become modules for rings of quadratic integers. Multiplication of these lattices by nonprincipal ideals yields simple constructions of further lattices including the Leech lattice.
## Abstract Conditions for a matrix to be totally unimodular, due to Camion, are applied to extend and simplify proofs of other characterizations of total unimodularity.
We say that a totally unimodular matrix is k-totally unimodular (k-TU), if every matrix obtained from it by setting to zero a subset of at most k entries is still totally unimodular. We present the following results. (i) A matrix is restricted unimodular if and only if it is 3-TU, (ii) for a 2-TU m