Further results on Hermitian algebras derived from Latin squares with potential applications to physics and chemistry: unitary matrices that diagonalize the algebras (Q2382898)

Earlier the author presented an infinite class of algebras of Hermitian matrices [ibid. 129, No. 1--2, 305--316 (2005; Zbl 1059.05025)]. Each of these algebras were derived from latin squares. In this paper it is shown how to obtain a unitary matrix \(U\) (over the complex field) such that \(\widetilde{U}MU\) is a diagonal matrix, for all matrices \(M\) belonging to a particular algebra. The mentioned diagonal matrix is a matrix that contains the characteristic roots of \(M\). The matrix \(U\) may be different for different algebras. Many other related results are also presented.