A note on %26quot;Methods for constructing distance matrices and the inverse eigenvalue problem%26quot;

作者：Jaklic Gasper; Modic Jolanda^*

来源：Linear Algebra and Its Applications, 2012, 437(11): 2781-2792.

DOI：10.1016/j.laa.2012.06.044

• Symmetric nonnegative inverse eigenvalue problem
• Perron eigenvector
• Euclidean distance matrix

In this paper, a symmetric nonnegative matrix with zero diagonal and given spectrum, where exactly one of the eigenvalues is positive, is constructed. This solves the symmetric nonnegative eigenvalue problem (SNIEP) for such a spectrum. The construction is based on the idea from the paper Hayden, Reams, Wells, %26quot;Methods for constructing distance matrices and the inverse eigenvalue problem%26quot;. Some results of this paper are enhanced. The construction is applied for the solution of the inverse eigenvalue problem for Euclidean distance matrices, under some assumptions on the eigenvalues.

• 出版日期2012-12-1