Concerning the description of nonnegative normal matrices (Q1281228)

Some questions from the theory of matrices are considered. In the recent publication by \textit{S. K. Jain} and \textit{L. E. Snyder} [Linear Algebra Appl. 182, 147-155 (1993; Zbl 0768.15017)] a description of nonnegative matrices \(A\) for which a conjugate matrix \(A^T\) has the form of a polynomial \(f(A)\) was given. It was noted that all coefficients of this polynomial must be nonnegative and the constant term must be equal to zero. Here it is shown that the abovementioned result is a simple consequence of the classical Frobenius' theorem. Then the whole class of nonnegative normal matrices is analyzed. The analysis allows to suggest that the most natural description of the given class may be derived in terms of symmetric and antisymmetric components of the proper matrices.