Fiedler Matrices and Their Factorization

Let A be an m × n real matrix with m \u3e n such that the submatrix of A consisting of the first n rows of A is a nonsingular, lower triangular matrix and such that the submatrix of A consisting of the last n rows of A is a nonsingular, upper triangular matrix. Miroslav Fiedler introduced such matrices and called them column-rhomboidal. The structure and properties of column stochastic, centrosymmetric, column-rhomboidal matrices with constant row sums is examined. These matrices are called Fielder matrices. In particular, the factorization of Fielder matrices into Fiedler matrices is investigated