×

Trace, symmetry and orthogonality. (English) Zbl 0838.05020

The author uses the trace function to obtain easy proofs to two important questions in the theory of combinatorial matrices. He develops a new simple proof that there is no circulant conference matrix of order \(> 2\) and obtains new results concerning the existence of symmetric Hadamard matrices with constant diagonal. It is shown that there are \(2^t\) disjoint amicable weighing matrices of order \(2^t p\), where \(p\) is odd and that this is an upper bound for \(t\leq 1\). He obtains stronger bounds in certain other cases.

MSC:

05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
15A15 Determinants, permanents, traces, other special matrix functions
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
PDFBibTeX XMLCite
Full Text: DOI