Note on nonnegative matrices
- 1 May 1970
- journal article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 25 (1) , 80-82
- https://doi.org/10.1090/s0002-9939-1970-0257114-x
Abstract
Let A A be a nonnegative square matrix and B = D 1 A D 2 B = {D_1}A{D_2} where D 1 {D_1} and D 2 {D_2} are diagonal matrices with positive diagonal entries. Several proofs are known for the following theorem: If A A is fully indecomposable then D 1 {D_1} and D 2 {D_2} can be chosen so that B B is doubly stochastic. Moreover, D 1 {D_1} and D 2 {D_2} are unique up to a scalar factor. It is shown that these results can be easily obtained by considering a minimum of a certain rational function of several variables.Keywords
This publication has 4 references indexed in Scilit:
- Concerning nonnegative matrices and doubly stochastic matricesPacific Journal of Mathematics, 1967
- Reduction of a Matrix with Positive Elements to a Doubly Stochastic MatrixProceedings of the American Mathematical Society, 1967
- The diagonal equivalence of a nonnegative matrix to a stochastic matrixJournal of Mathematical Analysis and Applications, 1966
- A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic MatricesThe Annals of Mathematical Statistics, 1964