Special Issue on Positivity in Linear Algebra
Positivity in linear algebra arises in many different forms and flavors. It includes the study of matrices with nonnegative entries (Perron-Frobenius theory), matrices with positive principle minors (P-matrices, positive definite matrices, totally positive matrices), as well as linear maps with characteristics that generalize or combine these notions of positivity (e.g., positive operators, cone preserving maps).
The applications of positivity as a linear algebraic notion are indeed numerous, ranging from the physical and social sciences to other mathematical areas like graph theory, optimization, stochastic processes, statistics, dynamical systems and numerical analysis. The benefit is mutual as many advances in these areas are being achieved with the aid of linear algebra and its notions of positivity, which in turn are enriched by ideas, challenges and goals for the future.
For this special issue, we are looking for papers that primarily advance knowledge about positivity in linear algebra and the associated matrix classes, or that extend the reach of their theory in applications and in other mathematical fields.
Areas and topics of interest include, but are not limited to the following:
Entrywise positive (nonnegative) matrices. M-matrices and their inverses. Eventually nonnegative matrices. Positive (semi-)definite matrices. Totally positive (nonnegative) matrices. P-matrices. Cone preserving maps. Positive stability. Generalizations of the above in the context of operator theory and matrix functions.