Methods for constructing distance matrices and the inverse eigenvalue problem
Necessary conditions are provided on \(Z\) in order that \(D=\left[ \begin{smallmatrix} D_1 & Z\\ Z^T & D_2\end{smallmatrix}\right]\in\mathbb{R}^{n\times n}\) is a distance matrix \((D_1,D_2\) are distance matrices). To construct an \((n+1) \times (n+1)\) distance matrix it is always possible to border an \(n\times n\) distance matrix with certain scalar multiples of the Perron eigenvector. Necessary and sufficient conditions are obtained for the use of the Perron eigenvector related to the \(D_1\) and \(D_2\) blocks in the formation of the above distance matrix. The solution of the inverse eigenvalue problem is discussed. The case of the existence of a Hadamard matrix is included.
scientific article; zbMATH DE number 1371416