dedicated to professor w. t. tutte on the occasion of his eightieth birthday We characterize the symmetric (0, 1)-matrices that can be signed symmetrically so that every principal submatrix has determinant 0, \1. This characterization generalizes Tutte's famous characterization of totally unimodula
On totally unimodular matrices
โ Scribed by A. Tamir
- Publisher
- John Wiley and Sons
- Year
- 1976
- Tongue
- English
- Weight
- 431 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0028-3045
No coin nor oath required. For personal study only.
โฆ Synopsis
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.
๐ SIMILAR VOLUMES
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
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.
## Intervals of Totally Nonnegative and Related Matrices We consider the class of the totally nonnegative matrices, i.e., the matrices having all their minors nonnegative, and intervals of matrices with respect to the chequerboard partial ordering, which results from the usual entrywise partial or