Projects per year
Abstract
A trade in a complex Hadamard matrix is a set of entries which can be changed to obtain a different complex Hadamard matrix. We show that in a real Hadamard matrix of order n all trades contain at least n entries. We call a trade rectangular if it consists of a submatrix that can be multiplied by some scalar c ≠ 1 to obtain another complex Hadamard matrix. We give a characterisation of rectangular trades in complex Hadamard matrices of order n and show that they all contain at least n entries. We conjecture that all trades in complex Hadamard matrices contain at least n entries.
Original language  English 

Title of host publication  Algebraic Design Theory and Hadamard Matrices 
Subtitle of host publication  ADTHM, Lethbridge, Alberta, Canada, July 2014 
Editors  Charles J Colbourn 
Place of Publication  Cham Switzerland 
Publisher  Springer 
Pages  213221 
Number of pages  9 
Volume  133 
ISBN (Electronic)  9783319177298 
ISBN (Print)  9783319177281 
DOIs  
Publication status  Published  3 Sept 2015 
Event  Workshop on Algebraic Design Theory and Hadamard Matrices 2014  University of Lethbridge, Alberta, Canada Duration: 8 Jul 2014 → 11 Jul 2017 https://link.springer.com/book/10.1007%2F9783319177298 
Publication series
Name  Springer Proceedings in Mathematics & Statistics 

Publisher  Springer 
Volume  133 
ISSN (Print)  21941009 
ISSN (Electronic)  21941017 
Conference
Conference  Workshop on Algebraic Design Theory and Hadamard Matrices 2014 

Abbreviated title  ADTHM 2014 
Country/Territory  Canada 
City  Alberta 
Period  8/07/14 → 11/07/17 
Internet address 
Keywords
 Hadamard matrix
 Trade
 Rank
Projects
 2 Finished

Towards the prime power conjecture
Australian Research Council (ARC), Monash University
27/02/12 → 31/12/16
Project: Research

Extremal Problems in Hypergraph Matchings
Wanless, I., Greenhill, C. & Aharoni, R.
Australian Research Council (ARC), University of New South Wales (UNSW)
3/01/12 → 31/12/14
Project: Research