On certain quasidiagonalizable families of matrices (Q1571189)

The authors show that the algebras of \((T+H)\)-circulants and skew-circulants constructed by \textit{E. Bozzo} [Linear Algebra Appl. 230, 127-150 (1995; Zbl 0839.15007)] are unitarily quasidiagonalizable. The algebra of Brownian matrices determined by \textit{M. J. C. Gover} [Linear Algebra Appl. 103, 87-102 (1988; Zbl 0644.15006)] is characterized as a centralizer. The family of retrocirculants is embedded into an algebra that is also interpreted as a centralizer. Polynomial identities are discussed as a tool for verifying quasidiagonalizability of matrix algebras in computer algebra applications.