Characterization of Positive Operators


  • Lucio Fassarella UFES


Positive operators, Routh-Hurwitz criterion, Characteristic Polynomial


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.


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.




How to Cite

Fassarella, L. 2023. Characterization of Positive Operators. Latin American Journal of Mathematics. 2, 01 (May 2023), 1–11.