“…Recently, there have been several studies about simultaneously diagonalizable real matrices. In particular, in investigating the preconditioning of Toeplitz matrices (see, e.g., [21]), several matrix algebras are considered, among which the class of all circulant matrices (see, e.g., [6], [15], [16], [17], [26], [32], [42], [45]), the family of all ω-circulant matrices (see, e.g., [7], [29]), the set of all τ-matrices (see, e.g., [8]) and the family of all matrices diagonalized by the Hartley transform (see, e.g., [3], [9], [12]).…”