# A sparsity result on nonnegative real matrices with given spectrum

Banach Center Publications (1997)

- Volume: 38, Issue: 1, page 187-191
- ISSN: 0137-6934

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topLaffey, Thomas. "A sparsity result on nonnegative real matrices with given spectrum." Banach Center Publications 38.1 (1997): 187-191. <http://eudml.org/doc/208627>.

@article{Laffey1997,

abstract = {Let σ=(λ1,...,λn) be the spectrum of a nonnegative real n × n matrix. It is shown that σ is the spectrum of a nonnegative real n × n matrix having at most $(n+1)^2/2-1$ nonzero entries.},

author = {Laffey, Thomas},

journal = {Banach Center Publications},

keywords = {nonnegative inverse eigenvalue; nonnegative matrix},

language = {eng},

number = {1},

pages = {187-191},

title = {A sparsity result on nonnegative real matrices with given spectrum},

url = {http://eudml.org/doc/208627},

volume = {38},

year = {1997},

}

TY - JOUR

AU - Laffey, Thomas

TI - A sparsity result on nonnegative real matrices with given spectrum

JO - Banach Center Publications

PY - 1997

VL - 38

IS - 1

SP - 187

EP - 191

AB - Let σ=(λ1,...,λn) be the spectrum of a nonnegative real n × n matrix. It is shown that σ is the spectrum of a nonnegative real n × n matrix having at most $(n+1)^2/2-1$ nonzero entries.

LA - eng

KW - nonnegative inverse eigenvalue; nonnegative matrix

UR - http://eudml.org/doc/208627

ER -

## References

top- [1] M. Boyle, Symbolic dynamics and matrices, in: Combinatorial and Graph-Theoretical Problems in Linear Algebra (eds. Brualdi, Friedland and Klee), IMA Vol. Math. Appl. 50 (1993), 1-38. Zbl0844.58023
- [2] D. Handelman, Spectral radii of primitive integral companion matrices and log concave polynomials, in: Symbolic dynamics and its applications, Contemp. Math. 135 (1992), 231-238. Zbl0771.12002
- [3] C. R. Johnson, Row stochastic matrices that are similar to doubly stochastic matrices, Linear and Multilinear Algebra 10 (1981), 113-120. Zbl0455.15019
- [4] R. Loewy and D. London, A note on the inverse problem for nonnegative matrices, Linear and Multilinear Algebra 6 (1978), 83-90. Zbl0376.15006
- [5] T. J. Laffey, Inverse eigenvalue problem for matrices, to appear in Hamilton Conference Proceedings, Royal Irish Academy. Zbl1280.15005
- [6] R. Reams, Topics in Matrix Theory, Thesis presented for the degree of Ph.D., National University of Ireland, 1994.

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