Inverse eigenvalue problem of nonnegative matrices via unit lower triangular matrices (Part I)

Document Type : Research Article


Department of Mathematics, Arak University, P.O. Box 38156-8-8943, Arak, Iran


This 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.


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