Characterization of Positive Operators
DOI:
https://doi.org/10.14244/lajm.v2i01.12Keywords:
Positive operators, Routh-Hurwitz criterion, Characteristic PolynomialAbstract
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
Hurwitz A. Uber die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen Teilen besitzt. Mat Ann. 1895; 46: 273–284.
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.
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.
Lewin M. On the coefficients of the characteristic polynomial of a matrix. Discrete Mathematics. 1994; 125: 255–262.
Collings BJ. Characteristic polynomial by diagonal expansion. The American Statistician. 1987; 37(3): 233–235.
Pennisi LL. Coefficients of the Characteristic Polynomial. Mathematics Magazine. 1987; 60: 31–33.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Lucio Fassarella
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors may enter into separate contractual agreements for the non-exclusive distribution of the journal's published version of the work (for example, posting it in an institutional repository or publishing it in a book), with an acknowledgment of its initial publication in this journal.
