Essentially doubly stochastic matrices
Eugene C. Johnsen · Linear and Multilinear Algebra · 1973
In this paper the following analogue to a well-known result in ordinary matrix theory is proved. Every nonsingular essentially doubly stochastic (e.d.s.) matrix of order n: with entries from a field F:,char(F)=0 or char(F)>n, is a product of nonsingular elementary e.d.s. matrices. This is then extended to the following more general result. Every e.d.s. matrix of order n: and rank r:, 1> r:>n:, with entries from a field F:, char(F:)=0 or char(F:)>n:, is a product of elementary e.d.s. matrices. This product has nm‐ r singular factors, the number n:m‐r: being minimal, and all of them may be taken to be a particular singular elementary e.d.s. matrix.