The Inverse Eigenvalue Problem for Tridiagonal Matrices With Linear Relation

2009 ◽  
Author(s):  
Zhibin Li ◽  
Xinxin Zhao
Keyword(s):  
Eigenvalue Problem ◽  
Linear Relation ◽  
Inverse Eigenvalue Problem ◽  
Tridiagonal Matrices ◽  
Inverse Eigenvalue

Inverse Eigenvalue Problem for a Class of Upper Triangular Matrices with Linear Relation

2014 ◽  
Vol 668-669 ◽  
pp. 1068-1071
Author(s):  
Zhi Bin Li ◽  
Shuai Li
Keyword(s):  
Eigenvalue Problem ◽  
Linear Relation ◽  
Existence And Uniqueness ◽  
Triangular Matrix ◽  
Inverse Eigenvalue Problem ◽  
Triangular Matrices ◽  
Numerical Example ◽  
Upper Triangular Matrices ◽  
Inverse Eigenvalue ◽  
Upper Triangular Matrix

This paper studies on the eigenvalue[1-5] of the a class of upper triangular matrix with linear relation. It discusses the feature of existence and uniqueness of matrix via two given two characteristic pairs(λ,χ),(μ,γ) . Solutions and expressions are provided under satisfied conditions. The possibilities are exanimated by numerical example.

scholarly journals An inverse eigenvalue problem for symmetrical tridiagonal matrices

2007 ◽  
Vol 54 (5) ◽  
pp. 699-708 ◽  
Author(s):  
Hubert Pickmann ◽  
Ricardo L. Soto ◽  
J. Egaña ◽  
Mario Salas
Keyword(s):  
Eigenvalue Problem ◽  
Inverse Eigenvalue Problem ◽  
Tridiagonal Matrices ◽  
Inverse Eigenvalue

scholarly journals Toeplitz nonnegative realization of spectra via companion matrices

2019 ◽  
Vol 7 (1) ◽  
pp. 230-245
Author(s):  
Macarena Collao ◽  
Mario Salas ◽  
Ricardo L. Soto
Keyword(s):  
Eigenvalue Problem ◽  
Half Plane ◽  
Toeplitz Matrix ◽  
Toeplitz Matrices ◽  
Nonnegative Matrix ◽  
Inverse Eigenvalue Problem ◽  
Complex Numbers ◽  
Inverse Eigenvalue ◽  
Companion Matrices ◽  
Solution Matrix

Abstract The nonnegative inverse eigenvalue problem (NIEP) is the problem of finding conditions for the existence of an n × n entrywise nonnegative matrix A with prescribed spectrum Λ = {λ1, . . ., λn}. If the problem has a solution, we say that Λ is realizable and that A is a realizing matrix. In this paper we consider the NIEP for a Toeplitz realizing matrix A, and as far as we know, this is the first work which addresses the Toeplitz nonnegative realization of spectra. We show that nonnegative companion matrices are similar to nonnegative Toeplitz ones. We note that, as a consequence, a realizable list Λ= {λ1, . . ., λn} of complex numbers in the left-half plane, that is, with Re λi≤ 0, i = 2, . . ., n, is in particular realizable by a Toeplitz matrix. Moreover, we show how to construct symmetric nonnegative block Toeplitz matrices with prescribed spectrum and we explore the universal realizability of lists, which are realizable by this kind of matrices. We also propose a Matlab Toeplitz routine to compute a Toeplitz solution matrix.

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