The following inverse spectrum problem for nonnegative matrices is considered: given a set of complex numbers σ = {λ 1 , λ 2 , . . . , λ n }, find necessary and sufficient conditions for the existence of an n × n nonnegative matrix A with spectrum σ . Our work is motivated by a relevant theoretical
Construction of nonnegative symmetric matrices with given spectrum
✍ Scribed by Thomas J. Laffey; Helena Šmigoc
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 157 KB
- Volume
- 421
- Category
- Article
- ISSN
- 0024-3795
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We consider the following inverse spectrum problem for nonnegative matrices: given a set of real numbers σ = {λ 1 , λ 2 , . . . , λ n }, find necessary and sufficient conditions for the existence of an n × n nonnegative matrix A with spectrum σ . In particular, by the use of a relevant theorem of Br
We prove by explicit construction the existence of at least one nontrivial symmetric hyperdominant matrix with assigned nonnegative spectrum. In addition, we construct symmetric matrices with assigned spectra and several specific nonhyperdominant types of sign patterns.