ON A GENERALIZATION OF SOULES BASES

摘要

We characterize ordered orthonormal bases{s1, sn} C R~n for which the matrix is nonnegative for each t = 1,,n. In particular we show that the associatedorthogonal matrix S = [8_1, 8_2,, s_n]has certain submatrices that are Soules matrices. Based onthe construction of Soules bases developed by Elsner, Nabben, and Neumann [Linear Algebra AppI.,271 (1998), pp. 323-343] we are able to construct all possible such bases. Additionally, we showthat this set is the closure of the set of Smiles bases. We also include some results regarding matrixfunctions of SAST, where A is a diagonal matrix with nonincreasing diagonal entries.