Event № 209
Supervisor: Professor Emeritus Raphael Loewy
Abstract: Nonnegative matrices are important in many areas. Of particular importance are the spectral properties of square nonnegative matrices. Some spectral properties are given by the well-known Perron-Frobenius theory, which is about 100 years old. One of the most difficult problems in matrix theory is to determine the lists of $n$ complex numbers (respectively real numbers) which are the spectra of $ n \times n $ nonnegative (respectively symmetric nonnegative) matrices. In fact, this problem is open for any $ n \geq 5 $. Our work deals with the first open case, that is $ n = 5 $, for a list of real numbers. We made a significant progress towards the solution of this case. In particular, we obtain the solution when the sum of the five given numbers is zero or at least half of the largest one.