University of Guilan Journal of Mathematical Modeling 2345-394X 11 3 2023 10 01 On the inverse eigenvalue problem for a specific symmetric matrix 479 489 6649 10.22124/jmm.2023.24068.2151 EN Maryam Babaei Zarch Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Kerman, Iran Journal Article 2023 03 09 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. eigenvalue eigenpair leading principal submatrices Inverse eigenvalue problem https://jmm.guilan.ac.ir/article_6649_706dd14155c64d4d9a3f2ce65a6394d4.pdf