Open AccessThe Non-negative Inverse Eigenvalue Problem for Tridiagonal Matrix, Circulant Matrix and Symmetric Matrix
Author(s) -
Pengyu Zhu,
Yingjing Yong,
Zhang Guo,
Baicheng Ren
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1848/1/012011
Subject(s) - circulant matrix , tridiagonal matrix , matrix (chemical analysis) , mathematics , eigenvalues and eigenvectors , involutory matrix , centrosymmetric matrix , inverse , symmetric matrix , band matrix , hollow matrix , single entry matrix , integer matrix , nonnegative matrix , combinatorics , square matrix , pure mathematics , algebra over a field , physics , geometry , quantum mechanics , materials science , composite material
The Non-negative Inverse Eigenvalue Problem (NIEP) is a sub-problem extracted from inverse eigenvalue problem with a long history from 1930s determining the sufficient and necessary conditions in order that, σ={ λ 1 ,…, λ n }to be the spectrum of an entry wise non-negative n x n matrix. There had been many excellent researchers and scholars who contributed to discover many practical theories. The following of this paper would be then separated into two parts to further analyze the NIEP. In the first section of the paper, some important preexisting conclusions would be demonstrated and the groups’ understanding of these indispensable theories would be expressed. In the second section, three special and wildly used matrix, including tridiagongal matrix, circulant matrix, and symmetric matrix would be considered. The solution of the NIEP of these matrices done by the group would be expressed.