Characterization of Positive Operators

Authors

  • Lucio Fassarella UFES

DOI:

https://doi.org/10.14244/lajm.v2i01.12

Keywords:

Positive operators, Routh-Hurwitz criterion, Characteristic Polynomial

Abstract

A characterization of positive operators on finite dimensional complex vector spaces, developed from the Routh-Hurwitz criterion with review of some basic concepts and results.

References

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Gantmacher FR. Applications of the Theory of Matrices. Interscience Publishers Inc.; 1959.

Johnson CR, Tarazaga P. A Characterization of Positive Matrices. Positivity. 2005; 9: 149–150. DOI: https://doi.org/10.1007/s11117-005-7076-y

Fong CK, Tsui SK. A Note on Positive Operators. J Operator Theory. 1981; 5: 73–76.

Halmos PR. Finite Dimensional Vector Spaces. Springer-Verlag; 1997.

Halmos PR. Introduction to Hilbert Space and the Theory of Spectral Multiplicity. Chelsea Publiching Company; 1951.

Conway JB. A Course in Functional Analysis. Springer-Verlag; 1985. DOI: https://doi.org/10.1007/978-1-4757-3828-5

Lewin M. On the coefficients of the characteristic polynomial of a matrix. Discrete Mathematics. 1994; 125: 255–262. DOI: https://doi.org/10.1016/0012-365X(94)90166-X

Collings BJ. Characteristic polynomial by diagonal expansion. The American Statistician. 1987; 37(3): 233–235. DOI: https://doi.org/10.1080/00031305.1983.10483111

Pennisi LL. Coefficients of the Characteristic Polynomial. Mathematics Magazine. 1987; 60: 31–33. DOI: https://doi.org/10.1080/0025570X.1987.11977272

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Published

05/10/2023

How to Cite

[1]
Fassarella, L. 2023. Characterization of Positive Operators. Latin American Journal of Mathematics. 2, 01 (May 2023), 1–11. DOI:https://doi.org/10.14244/lajm.v2i01.12.

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