Craigen, R. Trace, symmetry and orthogonality. (English) Zbl 0838.05020 Can. Math. Bull. 37, No. 4, 461-467 (1994). 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. Reviewer: J.R.Seberry (Wollongong) Cited in 5 Documents 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.) Keywords:symmetry; orthogonality; trace function; circulant conference matrix; Hadamard matrices; disjoint amicable weighing matrices; bound PDFBibTeX XMLCite \textit{R. Craigen}, Can. Math. Bull. 37, No. 4, 461--467 (1994; Zbl 0838.05020) Full Text: DOI