University of GuilanJournal of Mathematical Modeling2345-394X12120240301Inverse eigenvalue problem of nonnegative matrices via unit lower triangular matrices (Part I)117130735210.22124/jmm.2023.21759.2092ENAlimohammadNazariDepartment of Mathematics, Arak University, P.O. Box 38156-8-8943, Arak, Iran0000-0002-3231-0340AtiyehNezamiDepartment of Mathematics, Arak University, P.O. Box 38156-8-8943, Arak, IranJournal Article20221215This paper uses unit lower triangular matrices to solve the nonnegative inverse eigenvalue problem for various sets of real numbers. This problem has remained unsolved for many years for $n \geq 5.$ The inverse of the unit lower triangular matrices can be easily calculated and the matrix similarities are also helpful to be able to solve this important problem to a considerable extent. It is assumed that in the given set of eigenvalues, the number of positive eigenvalues is less than or equal to the number of nonpositive eigenvalues to find a nonnegative matrix such that the given set is its spectrum.https://jmm.guilan.ac.ir/article_7352_3f3b6276cb29703ff071720a7048095a.pdf