Quasi-Balanced Weighing Matrices
A matrix $W$ with entries in $\{0,1,-1\}$ for which $WW^{t} = pI_{n}$ is a weighing matrix of order $n$ and weight $p$. The weighing matrix $W$ is quasi-balanced if $|W||W|^{t} = |W|^{t}|W|$ has at most two off-diagonal entries, where $|W|_{ij} = |W_{ij}|$. A quasi-balanced weighing matrix $W$ signs a strongly regular graph if $|W|$ coincides with its adjacency matrix. A brief review including some signed strongly regular graphs and equivalent association scheme is presented.
This is joint work with Thomas Pender and Sho Suda.
Bio: Hadi Kharaghani is a mathematics professor at the University of Lethbridge and holds a 1975 Ph.D. from the University of Calgary.