Volume 22, Issue 4
On the General Algebraic Inverse Eigenvalue Problems

Yu-hai Zhang

DOI:

J. Comp. Math., 22 (2004), pp. 567-580

Published online: 2004-08

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  • Abstract

A number of new results on sufficient conditions for the solvability and numerical algorithms of the following general algebraic inverse eigenvalue problem are obtained: Given n+1 real$n\times n$ matrices $A=(a_{ij}),A_k=(a_{ij}^{(k)})(k=1,2,\cdots,n)$ and n distinct real numbers $\lambda_1,\lambda_2,\cdots,\lambda_n,$ find n real number $c_1,c_2,\cdots,c_n$ such that the matrix $A(c)=A+\sum\limits_{k=1}^{n}c_k A_k$ has eigenvalues $\lambda_1,\lambda_2,\cdots,\lambda_n.$

  • Keywords

Linear algebra Eigenvalue problem Inverse problem

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@Article{JCM-22-567, author = {}, title = {On the General Algebraic Inverse Eigenvalue Problems}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {4}, pages = {567--580}, abstract = { A number of new results on sufficient conditions for the solvability and numerical algorithms of the following general algebraic inverse eigenvalue problem are obtained: Given n+1 real$n\times n$ matrices $A=(a_{ij}),A_k=(a_{ij}^{(k)})(k=1,2,\cdots,n)$ and n distinct real numbers $\lambda_1,\lambda_2,\cdots,\lambda_n,$ find n real number $c_1,c_2,\cdots,c_n$ such that the matrix $A(c)=A+\sum\limits_{k=1}^{n}c_k A_k$ has eigenvalues $\lambda_1,\lambda_2,\cdots,\lambda_n.$ }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10306.html} }
TY - JOUR T1 - On the General Algebraic Inverse Eigenvalue Problems JO - Journal of Computational Mathematics VL - 4 SP - 567 EP - 580 PY - 2004 DA - 2004/08 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10306.html KW - Linear algebra KW - Eigenvalue problem KW - Inverse problem AB - A number of new results on sufficient conditions for the solvability and numerical algorithms of the following general algebraic inverse eigenvalue problem are obtained: Given n+1 real$n\times n$ matrices $A=(a_{ij}),A_k=(a_{ij}^{(k)})(k=1,2,\cdots,n)$ and n distinct real numbers $\lambda_1,\lambda_2,\cdots,\lambda_n,$ find n real number $c_1,c_2,\cdots,c_n$ such that the matrix $A(c)=A+\sum\limits_{k=1}^{n}c_k A_k$ has eigenvalues $\lambda_1,\lambda_2,\cdots,\lambda_n.$
Yu-hai Zhang. (1970). On the General Algebraic Inverse Eigenvalue Problems. Journal of Computational Mathematics. 22 (4). 567-580. doi:
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