The nonnegative inverse eigenvalue problem

On Open Problems of Nonnegative Inverse Eigenvalues Problem

“…pdf). Readers also may refer to [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] for some previous results. In some articles, some necessary conditions and sufficient conditions for the three problems above have been given under some small dimension or special cases [7].…”

“…In some articles, some necessary conditions and sufficient conditions for the three problems above have been given under some small dimension or special cases [7]. Also See the survey paper [26] and the book [2, Chapter VII]. The earliest study on the subject of NIEP was perhaps due to the Russian mathematician Suleimanova (1949) on stochastic matrices, followed by Perfect (1953Perfect ( , 1955.…”

Symmetric nonnegative realization of spectra

“…Then they show that S n = R n for n = 3 and n = 4. In In [3], Egleston et al study the symmetric realizability of lists of five numbers {1, λ 2 , . .…”

“…in the second case (see [3]) imply that Theorem 3.1 gives no information about the realizability of the list Λ = {1, λ 2 , . .…”

“…The same occurs if we take ω 1 = −λ 5 + S or ω 1 = −λ 5 + an extreme symmetric matrix with prescribed spectrum and show that one of these patterns yields to realizable points which have not been known previously. In [12] is presented a graph related with the second unresolved case in [3]. In particular this graph considers points of the form (1, λ 2 , λ 2 , λ 3 , λ 3 ), which are plotted with λ 2 on the horizontal axis and λ 3 on the vertical axis.…”