On the inverse eigenvalue problem for a specific symmetric matrix

Document Type : Research Article


Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Kerman, Iran


The aim of the current paper is to study a partially described inverse eigenvalue problem of  a specific symmetric  matrix, and prove some properties of such matrix. The problem includes the construction of the matrix by  the  minimal eigenvalue of all  leading principal submatrices  and eigenpair $(\lambda_2^{(n)},x)$ such that $ \lambda_2^{(n)}$ is the maximal eigenvalue of the required matrix. We investigate  conditions for the solvability of the problem, and finally an algorithm and  its numerical results are presented.


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