Applications of a Brauer theorem in the nonnegative inverse eigenvalue problem. (English) Zbl 1097.15014
The authors extend a realizability criterion presented by H. Perfect [Duke Math. J. 22, 305–311 (1955; Zbl 0068.32704)] for the real nonnegative inverse eigenvalue problem. This new criterion strictly contains the realizability criterion due to R. L. Soto [Linear Algebra Appl. 369, 169–184 (2003; Zbl 1031.15018)]. Realizability criteria for the \(5\times 5\) nonnegative inverse eigenvalue problem and in the symmetric case for one of the unsolved cases of P. D. Egleston, T. D. Lenker and S. K. Narayan [Linear Algebra Appl. 379, 475–490 (2004; Zbl 1040.15009)] and illustrative examples are provided.
Reviewer: C. M. da Fonseca (Coimbra)
MSC:
| 15A18 | Eigenvalues, singular values, and eigenvectors |
| 15A29 | Inverse problems in linear algebra |
| 15B48 | Positive matrices and their generalizations; cones of matrices |
| 65F18 | Numerical solutions to inverse eigenvalue problems |
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