An inverse eigenvalue problem for totally nonnegative matrices
- 1 January 1985
- journal article
- research article
- Published by Taylor & Francis in Linear and Multilinear Algebra
- Vol. 17 (1) , 19-23
- https://doi.org/10.1080/03081088508817638
Abstract
In a previous paper we proved that the diagonal elements of a totally nonnegative matrix are majorized by its eigenvalues. In this note we show that the majorization of a vector of nonnegative real numbers by another vector of nonnegative real numbers is not sufficient for the existence of a totally nonnegative matrix with diagonal elements taken from the entries of the majorized vector and eigenvalues taken from the entries of the majorizing vector.Keywords
This publication has 5 references indexed in Scilit:
- Majorization between the diagonal elements and the eigenvalues of an oscillating matrixLinear Algebra and its Applications, 1982
- Eigenvalues of nonnegative symmetric matricesLinear Algebra and its Applications, 1974
- Oszillationsmatrizen, Oszillationskerne und kleine Schwingungen mechanischer SystemePublished by Walter de Gruyter GmbH ,1960
- Matrices with Prescribed Characteristic Roots and Diagonal ElementsJournal of the London Mathematical Society, 1958
- Doubly Stochastic Matrices and the Diagonal of a Rotation MatrixAmerican Journal of Mathematics, 1954