Sinkhorn, Richard2022-06-222022-06-22197113683362https://hdl.handle.net/10657/9740If A is a nonnegative square matrix and X is a vector, then the Menon operator associated with A, denoted by TA, is defined by (TAX)i = (n/sigma over j=1 (A) ji (n/sigma over k=1 (A) jk (X)k)-1)-1. A close relation 18 known to exist between doubly stochastic matrices and Menon operators. The following problem is investigated: If each of E and F is a matrix, when is ETAF a Menon operator? It is conjectured, but not proven, that if A is a nonnegative square matrix satisfying certain criterion, and each of E and F is a nonnegative matrix such that ETAF is a Menon operator, then each of E and F is the product of a diagonal matrix with positive diagonal and a permutatibn matrix. This conjecture is supported by examples, and also by theorems which show that if A is doubly stochastic and ETA = TAE then either there is a number r such that rE is doubly stochastic or there is a permutation matrix P such that PtEP can be partitijned into a certain block form. A condition is defined on a doubly stochastic matrix which implies that ETA=TAE if and only if there is a number r such that rE is a permutation matrix.application/pdfenThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. Section 107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.Menon operatorsThesisreformatted digital