Ukrainian mathematical congress - 2009

Alimohammad Nazari (Arak university, Iran)

The inverse eigenvalue problem for symmetric special kind of matrices

In recent paper [1](Juan Peng, Xi-Yan Hu. Lei Zhang) two inverse eigenvalue problems are solved and in the order article [2](Hubert Pickmann, Juan Egana., Ricardo L. Soto), a correction, for one of the problems stated in the first article, has been presented as well. In this article, according to the article [2], a symmetric matrix solution which is different from the one in the article [1] has been presented for one of the problems which are in article [1]. The symmetric matrix solution in the article [1] and the one which is presented by us, in the main diagonal, are similar, but instead of first column and row, we valued arbitrary column and row, furthermore other element of the matrix are considered null. i.e. we construct the symmetric special matrix that its eigenvalues and an eigenvector corresponding to largest of eigenvalue are given. We extend the problem II of [1] for arbitrary row and column instead of the first row and column.