The maximum determinant of ± 1 matrices
✍ Scribed by M.G. Neubauer; A.J. Radcliffe
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 599 KB
- Volume
- 257
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
In this paper we study the maximal absolute values of determinants and subdeterminants of ±1 matrices, especially Hadamard matrices. It is conjectured that the determinants of ±1 matrices of order n can have only the values k • p, where p is specified from an appropriate procedure. This conjecture i
We prove that row reducing a quantum matrix yields another quantum matrix for the same parameter q. This means that the elements of the new matrix satisfy Ž . the same relations as those of the original quantum matrix ring M n . As a q corollary, we can prove that the image of the quantum determinan
We show that for n >~ 5 the maximum determinant of an n x n matrix of zeros and ones whose zeros form an acyclic pattern is [(n-1)/2] [(n-1)/2] and characterize the case of equality. 1 We are indebted to H.J. Ryser for some of the references in this paragraph.